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1 


NORMAL 


METHODS  OF  TEACHING 


OOHTAIiriNO 


i   BBIEF  STATEMENT  OF  THE  PRINCIPLE3  AND  METHODS  OF  THE  SCIENCE  AND 

ABT  OF  TEACHING,  FOB  THE  USE  OF  NORMAL  CLASSES  AND  PBIYATB 

STUDENTS  PBEPABINO  THEMSELVES  FOB  TEACHBBS. 


BY 


EDWARD  BROOKS,  A.  M.,  Ph.D., 

rORSCER  PRINCIPAL  OP  STATE  NORMAL  SCHOOL,  PENRSTLVANIA,  AND  AUTHOR  OT  A 

NORMAL  SERIES  OF  MATHEMATICS,  MENTAL  SCIENCE  AND  CULTURE, 

PHILOSOPHY  OF  ARITHMETIC,   ETC. 


*'That  divine  and  beautiful  thing  called  Teaching.'* 
**Tlke  object  of  aU  education  is  to  teach  people  to  think  for  themulvet.** 


PHILADELPHIA : 

NORMAL,  PUBLISHING   COMPANY. 

1889. 


Copyright,  1879, 
By  EDWARD  BROOKS,  A.  M. 


BY  THE  SAME  AUTHOR. 

I.  The  Normal  Series  of  Arithmetics. 

1.  Tlie  Standard  Series:  a  full  course. 

Four  books  :  New  Primary  22;  Elementary  45 ;  New  Mental 
a5:  New  Written  80. 

2.  Tlie  Union  Series;  a  sliorter  course. 

Two  books;  Union  Part  I,  25;  The  Normal  Union  90. 

II.  Normal  Elementary  Algebra, $1.10 

III.  Normal  Geometry  and  Trigonometry,           -        -  1.10 

IV.  Normal  Higher  Arithmetic, 1.25 

V.  The  Philosophy  of  Arithmetic.     ....  2.2.T 

VI.  Keys  containing  Methods  and  Models. 

SOWER,  POTTS  &  CO..  Publishers. 

530  MAUIvET  STREET,  PHILADELPHIA. 

Copies  mailed  on  receipt  of  prices  annexed,  and  introduced  into 
schools  for  one-third  less. 


ie«)ucA"^o?vi  nEP^i 


iNQriRKR  V.  *  P.  :o  . 

8TKRKOTYVKKS   i    FKIHTXU, 
LANCASTER,  PA. 


PREFACE. 


'T'EACHIXG  is  a  Science  and  an  Art.  It  embraces  a  system  of  truths 
that  admit  of  scientific  statement  and  may  be  woven  together  with 
the  thread  of  philosophic  principles.  As  such  it  may  be  taught  like 
other  sciences  and  arts,  and  may  thus  be  presented  in  a  book  to  be 
studied.  The  present  volume  is  the  result  of  an  earnest  attempt  to  give 
a  scientific  statement  to  the  subject  in  a  form  that  can  be  used  in  the 
training  of  teachers. 

Object. — The  work  is  designed  as  a  Text-Book  on  TencMng.  It  is  a 
work  to  be  studied  and  mastered  by  those  who  are  preparing  themselves 
to  teach  in  our  public  shools.  Several  good  books  on  the  subject  have 
been  written  from  the  standpoint  of  the  profession  for  professional 
readers ;  this  work  is  written  from  the  standpoint  of  the  class-room, 
for  those  who  are  being  trained  for  the  profession.  Its  design  is  not  so 
much  to  adorn  the  literature  of  the  profession  as  to  aid  in  building  up 
the  profession.  The  aim  has  been  to  prepare  a  work  suitable  for  the 
use  of  the  classes  in  our  Normal  Schools, — a  work  that  can  be  studied 
and  recited  like  a  text-book  on  grammar  or  arithmetic. 

Origin. — The  work  grew  up  in  the  class-room.  The  matter  was 
originally  prepared  for  my  own  "teaching  classes,"  and  has  been  used 
by  them  for  many  years.  Primarily,  it  was  given  orally  to  the  classes, 
the  pupils  being  required  to  write  down  only  the  leading  defini- 
tions and  principles  and  an  outline  of  the  discussions.  Recently 
it  became  necessary  to  divide  these  classes  and  place  them  in  charge 
of  assistant  teachers.  For  the  use  of  these  assistants  the  notes  were 
expanded  into  a  little  treatise  which  the  pupils  were  required  to  copy 
and  recite.  So  inconvenient  was  this,  and  so  much  valuable  time  was 
lost,  that  I  resolved  to  comply  with  the  request  of  teachers  and  pupils 
and  put  the  matter  in  a  form  for  publication. 

Importance. — The  need  of  such  a  text-book  cannot  be  questioned. 

(iiij 


54  1J43 


IV  PREFACE. 

The  subject  itself  demands  it.  Teaching  is  a  science  and  an  art,  and 
as  such  deserves  to  be  stated  in  a  scientific  form.  The  teachers  and 
students  of  Teaching  demand  it.  The  time  has  gone  by  when  talks 
and  lectures  on  the  subject  of  Teaching  will  meet  the  wants  of  Normal 
instruction.  The  pupils  need  a  book  which  they  can  study  and  recite; 
they  want  to  see  that  they  are  making  actual  progress  in  Teaching  as 
in  other  branches.  In  our  Normal  Schools  the  science  of  Teaching 
must  be  placed  alongside  of  the  other  branches  for  exactness  of  state- 
ment, if  it  is  to  be  respected  and  appreciated  by  students.  Close  study 
of  mathematics  and  general  talks  on  Teaching  will  never  give  pupils 
a  very  high  appreciation  of  tiie   Science  of  Teaching. 

We  need  such  a  work  also  for  the  teachers  not  attending  our  Normal 
Schools.  County  Superintendents  tell  young  teachers  to  read  and  study 
works  on  Teaching  ;  and  the  question  is,  what  shall  they  study?  "How 
can  we  prepare  ourselves  in  the  science  of  Teaching?"  is  the  question 
that  comes  up  from  every  part  of  the  State.  There  are  several  excel- 
lent works  on  the  subject ;  but  they  do  not  seem  to  be  adapted  to  their 
wants.  Some  are  too  profound  ;  and  others  are  deficient  in  systematic 
thought  and  statement.  There  seems  to  be  no  elementary  text-book  in 
which  they  can  find  that  systematic  and  concise  statement  of  definitions 
and  principles  and  detailed  description  of  practical  methods  of  teaching 
the  branches,  which  they  need.  It  is  the  hope  of  the  author  that  the 
present  work  may  meet  this  want,  and  supply  this  demand. 

Nature  and  Contents. — A  work  on  Teaching  should  be  moulded  by 
the  wants  of  the  student  of  Teaching.  The  student  needs  a  systematic 
and  comprehensive  view  of  the  entire  subject.  He  needs  carefully  pre- 
pared definitions  and  statements  of  the  different  divisions  and  topics. 
He  needs  a  clear  and  definite  statement  of  principles  which  he  may  fix 
in  his  mind,  and  which  become  as  germs  to  his  thought  and  practice  in 
teaching.  He  needs  to  be  able  to  give  clear  and  logical  discussions  of 
the  principles,  and  to  show  their  application  to  the  methods  adopted. 
He  needs  to  be  able  to  state  the  various  methods  of  teaching,  give  illus 
trations  of  these  methods  and  show  their  adaptation  to  the  different 
subjects.     He  needs  to   be   drilled  in   the  literatxtre  of  teaching,  to 


PREFACE. 


acquire  a  vocabulary  of  educational  expressions  that  convey  to  his 
mind  definite  ideas  like  the  terms  and  definitions  of  grammar  and  arith- 
metic. The  student-teacher  should  study  these  until  they  become  part 
of  his  educational  vocabulary,  as  a  student  of  law  studies  Blackstone 
until  he  becomes  habituated  to  legal  forms  of  thought  and  expression. 

The  work  aims  to  meet  all  these  requirements.  It  presents,  first,  a 
scheme  of  a  complete  system  of  education,  the  principles  on  which  it  is 
based,  and  the  nature  and  laws  of  its  two  principal  divisions,  Culture 
and  Instruction.  It  presents,  second,  a  detailed  description  of  the 
methods  of  teaching  the  different  Irranches  of  study.  In  discussing 
these  Methods,  it  gives,  first,  a  description  of  the  general  nature  of 
each  branch,  and  second,  the  methods  of  teaching  it.  Tlie  former  divis- 
ion embraces  a  statement  of  the  philosophical  character  of  the  branch 
and  its  historical  development's,  both  of  which  are  of  great  value,  since 
the  nature  of  a  branch  determines  the  method  of  teaching  it,  and  the 
historic  order  of  its  growth  often  indicates  the  order  in  which  it  should 
be  developed  in  the  pupil's  mind.  The  methods  of  teaching  each 
branch  include,  first,  the  principles,  which  should  guide  the  teacher 
in  his  work  ;  second,  the  several  methods  that  may  be  employed,  indi- 
cating the  correct  method  ;  and  third,  descriptions  and  illustrations 
for  actual  model  lessons  in  the  branches. 

The  Style.— ks,  the  work  is  designed  for  a  text-book,  special  pains  have 
been  taken  to  employ  a  simple,  clear,  and  concise  style.  All  rhetorical 
ornament  and  diffuseness  of  description  have  been  carefully  avoided, 
and  the  attempt  made  to  reduce  the  matter  to  a  scientific  form,  and  to 
state  it  in  brief  and  simple  sentences  suitable  for  recitation.  The  author 
has  endeavored  to  keep  his  classes  of  pupils  before  his  mind,  and  aimed 
to  adapt  his  statements  to  their  comprehension  and  powers  of  express- 
ion. Nearly  every  paragraph  has  been  written  in  view  of  the  thought. 
How  will  this  answer  for  pupils  to  study  and  recite?  The  object  has 
been,  not  to  talk  about  the  subject,  but  to  embody  the  subject  in  Ian 
guage,  and  thus  make  a  text-book  on  Teaching. 

Correctness  of  Methods.— li  is  believed  that  the  principles  and  meth- 
ods presented  are  not  mere  theories ;   nearly  all  of  them  have  been 


Vi  PEEFACE. 

tested  by  actual  experience  in  the  class-room.  There  is  scarcely  a 
method  suggested  that  I  have  not  either  tested  myself,  or  had  tested  by 
my  teachers  in  our  Normal  or  Model  School  ;  and  hundreds  of  teachers 
have  introduced  them  into  the  public  schools  of  the  State  and  proved 
their  correctness  by  successful  teaching.  Many  of  the  methods  are  used 
by  the  leading  teachers  of  the  country,  and  are  generally  accepted  as 
correct.  For  any  methods  presented  which  may  seem  novel,  and  in 
advance  of  popular  practice,  I  ask  an  impartial  consideration,  believ- 
ing that  if  tried,  they  will  also  prove  to  be  worthy  of  acceptance. 

Origin  of  Matter. — In  the  preparation  of  the  work,  no  attempt  has 
been  made  to  be  merely  original.  The  object  has  been  to  present  the 
subject  as  it  lies  in  my  own  mind  and  as  it  is  thought  it  should  be  con 
ceived  by  young  people  preparing  to  teach.  The  subject  has  devel- 
oped itself  in  its  present  form  through  years  of  reading,  reflection,  and 
experience  ;  and  it  is  impossible  to  separate,  even  if  it  were  necessary, 
■what  has  been  acquired  from  that  which  is  the  product  of  the  author's 
own  thought.  Whenever  I  am  conscious  of  following  anything  peculiar 
to  another  author,  an  acknowledgment  is  made  ;  and  it  is  possible  that 
credit  should  have  been  given  in  some  cases  where  it  has  been  with- 
held. The  historical  facts  have  been  taken  from  various  sources,  and, 
in  some  cases,  the  language  has  been  partially  followed. 

In  closing  this  preface,  I  desire  to  express  the  hope  that  the  book, 

though  written  specially  for  my  own  pupils,  may  be  of  value  to  many 

of  the  young  teachers  of  our  country  ;  and  that  it  may  aid  in  lifting  up 

the  practice  of  teaching  to  a  higher  plane,  and  afford  means  for  that 

professional  culture  now  so  generally  demanded.     Having  written  the 

work  in  the  interests  of  teachers,  I  shall  find  my  highest  reward  in  the 

knowledge  that  it  has  proved  a  benefit  to  teachers,  and  done  something 

towards  building  up  one  of  the  best  and  noblest  interests  of  society— 

the  Profession  of  Teaching. 

EDWARD  BROOKS. 

Normal  School,  MUlersmlle,  Pa, 
i/a^  10, 1879. 


TABLE    OF    CONTENTS. 


Pbefacb  ...•••• 

PAKT    I. 
GENERAL  NATURE  OF  EDUCATION. 

CHAPTER  I. 
The  Nature  of  Educatiox  ..... 

CHAPTER  n. 

Gexeral,  Pbinciples  of  Education 


CHAPTEIi  III. 


The  Science  of  TEAcaixo 


CHAPTER  IV. 


The  Natuke  of  the  Mind     . 


CHAPTER  V. 


The  Nature  of  Culture 


CHAPTER  VI. 
Methods  of  Cultivating  Each  Faculty  . 

CHAPTER  VII. 
The  Nature  of  Knowledge 

CHAPTER  Vm. 
The  Forms  of  Instruction  . 


CHAPTER  IX. 


The  Okdeu  of  Ixsthuction 


CHAPTER  X. 
The  Printtpt-es  of  Txptrt'ction. 

I.  Principles  Derived  from  the  Nature  of  the  Mind    . 

II.   Principles  Derived  from  the  Nature  of  Knowledge 

III.  PriiK-ipKs  Derived  fiom  the  Nature  of  Instruction 

(vii) 


PASK 

.     iii 


13 

.    18 

86 
.    31 

87 
.    42 

48 
.    53 

ST 


.    «3 

67 

.    72 


vai 


CONTENTS. 


PART   II. 


TEACHING  THE    BRANCHES. 


I,   OBJECT  I.ESSONS. 


CHAPTER  I. 

The  Nature  of  Object  Lessons. 
I.  Value  of  Object  Lessons 
II.  Preparation  for  Object  Lessons 

III.  Method  of  Giving  Object  Lessons    . 

IV.  Errors  to  be  Avoided  in  Object  LessoiiS 
V.  Course  of  Instruction  in  Object  Lessons 

L  Lessons  on  Form 

2.  Lessons  on  Color 

3.  Objects  and  their  Parts    . 

4.  Qualities  of  Objects  .  • 

5.  Elements  of  Botany       .  . 


•                 1 

k 

.    79 

• 

• 

82 
.    83 

• 

• 

85 
.    85 

• 

• 

• 

a5 

.     86 

* 
• 

• 

89 
.    91 

• 

92 

II.    LANGUAGE. 

CHAPTER  I. 
The  Nature  of  Language  .  .  •  • 

I.  Spoken  Language       .  .  •  • 

n.  Written  Language  .  .  •  ■ 

HI.  Course  in  Language  .  •  • 

CHAPTER  n. 
Teaching  a  Child  to  Read. 

I.  Methods  of  Teaching  a  Child  to  Read    . 

n.  The  True  Method  of  Teaching  a  Child  to  Read 

CHAPTER  m. 
Teaching  the  Alphabet. 

I.  The  Nature  of  the  Alphabet        .  .  . 

II.  Methods  of  Teaching  the  Alphab^st  i 

CHAPTER  IV. 
Teaching  Pronunciation. 

I.  Nature  and  Importance  of  Pronunciation  . 

n.  Methods  of  Teaching  Pronunciation  . 

m.  Teachine  Correct  Pronunciation 


9» 

94 

95 

105 


107 
110 


118 
123 


127 
129 
135 


CONTENTS.  IX 

CHAPTER  V. 

FeACHIXG  OuTnOnKAPHT.  PAGE. 

I.  The  Nature  of  Ortlios:raphy  .  .  .  .  •   146 

II.  Metliods  ol  Teaching  Orthography        ....         152 

III.  The  Written  Method  of  Teaching  Orthography    .  .  .155 

IV.  The  Oral  Method  of  Teaching  Orthography     .  .  .158 
V.  General  Suggestions  in  Teaching  Orthography      .            .  .163 

CHAPTER  VI. 
TEACHiifG  Reading  .......        168 

I.  Tlie  Mental  Element  in  Reading     .....  172 

II.  The  Vocal  Element  in  Reading  .  .  .  .176 

III.  The  Physical  Element  in  Reading  .  .  .  .  .200 

CHAPTER  Vn. 
Teaching  Lexicoi-ogt       .......        21i 

CHAPTER  Vni. 
Teaching  English  Grammar  ......  221 

I.  General  Nature  of  the  Subject    .....        222 

II.  Methods  of  Teaching  Primary  Grammar    ....  239 
III.  Methods  of  Teaching  Advanced  Grammar      .  .  .        266 

CHAPTER  IX, 
Teaching  Composition         .......  286 

I.  Preparation  for  Composition  Writing    ....        288 

n.  Language  Lessons     .......  296 

III.  The  Writing  of  a  Composition    .....        301 

III.  MATHEMATICS. 

CHAPTER  I. 
The  Natitre  of  Mathematics  ......  819 


324 


CHAPTER  n. 
The  Nature  of  Arithmetic        ..... 

I.  The  General  Nature  of  Arithmetic  .  .  .  .  .325 

II.  The  Language  of  Arithmetic      .....        329 

III.  The  Reasoning  of  Arithmetic  .....  334 

IV.  The  Treatment  of  Arithmetic      .  ,  .  .  .339 
V.  The  Course  in  Arithmetic    ......  342 


345 


CHAPTER  m. 
Teaching  Phimakt  Aiutiimetic  ..... 

I.  Teaching  Arithmetical  Language     .  .  .  '  •  34:7 

II.  Teachino;  Addition  and  Sutttraction       ....        353 


X  CONTENTS. 

FAOS. 

III.  Teaching  Multiplication  and  Division         ....  359 

IV.  Teaefiing  Common  Fractions     .....        367 
V.  Teaching  Denominate  Numbers      .....  374 

CHAPTER  IV. 
Teachixg  Men'tai,  Arithmetic. 

I.  Importance  of  Mental  Arithmetic  ....        378 

II.  The  Nature  of  Mental  Arithmetic    .....  382 
III.  Methods  of  Teaching  Mental  Arithmetic  .  .  .        3S6 

CHAPTER  V. 
Teaching  Written  Arithmetic. 

I.  The  Nature  of  Written  Arithmetic  .  .  .  ,393 

II.  Methods  of  Teaching  Written  Arithmetic        .  .  .398 

CHAPTER  VI. 
Teaching  Geometry. 

I.  The  Nature  of  Geometry      .....  .404 

U.  Teaching  the  Elements  of  Geometiy     ....        409 

III.  Teaching  Geometry  as  a  Science     .  .  •  •  .  422 

CHAPTER  Vn. 
Teaching  Algebra. 

I.  The  Nature  of  Algebra 432 

II.  Method  of  Teaching  Algebra  .....  440 

IV.   PHYSICAIL  SCIBNCC 

CHAPTER  I. 
The  Nature  of  Physical  Scien«ce  •  .  .  .  .  449 

CHAPTER  n. 
Teaching  Geography. 

I.  The  Nature  of  Geography    .  .....  460 

II.  Teaching  Primary  Geography    .....        466 

III.  Teaching  Advanced  Geography       .  .  •  .  .  479 

IV.  Teaching  Physical  Geography    .....        483 

V.   HISTORY. 

CHAPTER  I. 
Teaching  History. 

I.  The  Nature  of  History  and  the  Course        ....  485 
n.  Teaching  the  Elements  of  History         .  .  •  .        490 

in.  Teaching  Advanced  History  .....  49.5 


PART  I. 

INTRODUCTION. 


NATURE  OF  EDUCATION. 


I.    The  Nature  op  Education. 
II.    General  Principles  of  Education. 

III.  The  Science  of  Teaching. 

IV.  The  Nature  of  the  Mind. 
v.    The  Nature  of  Culture. 

VI.    The  Culture  of  Each  Facultt. 
VII.     The  Nature  op  Knowledob. 
VIII.    The  Forms  op  Instruction. 
IX.    The  Order  op  Instruction. 
X.    The  Principles  of  Instruction, 


NORMAL 

METHODS  OF  TEACHING. 


CHAPTER  I. 

THE   NATURE   OF   EDUCATION. 

EDUCATION  treats  of  the  developing  of  the  powers  of 
man  and  the  furnishing  of  his  mind  with  knowledge. 
The  term  education  is  derived  from  educare,  to  teach,  which 
is  from  educere,  to  lead  out,  which  is  from  e,  out,  and  duco, 
I  lead. 

The  primary  idea  of  education,  as  shown  by  the  origin  of 
the  term,  seems  to  be  the  developing  or  drawing  out  of  the 
powers  of  the  mind ;  and  it  has  been  supposed  that  this  was 
its  earliest  use.  It  is  said  to  be  doubtful,  however,  whether 
the  Romans  ever  used  the  word  in  this  sense,  though  most 
modem  writers  have  so  understood  it.  The  term  has,  at  the 
present  day,  so  broadened  its  meaning  as  to  embrace  both  the 
development  of  man's  powers  and  the  furnishing  of  his  min:' 
with  knowledge. 

Proble^n  of  Education.— The  problem  of  education  em 
braces  several  distinct  elements,  as  will  appear  from  the 
following  analysis.  First,  there  must  be  a  being  to  be  edu- 
cated ;  this  being  is  Man.  Second,  there  must  be  something 
with  which  to  educate  man,  some  material  to  be  used  in  the 
educational  process;  this  material,  consisting  of  ideas,  facts, 
truths,  and  sentiments,  may  be  called  the  flatter  of  education. 

(13) 


14  METHODS   OF   TEACHING. 

Third,  there  must  be  some  wa}'  in  which  these  two  elements 
are  united  in  the  educational  process ;  this  wa}^  (methodos,  a 
way)  gives  rise  to  the  3Iethods  of  Education. 

The  problem  of  education  is  thus  seen  to  embrace  three 
elements — 3fan,  Matter^  and  Method.  Man  is  the  subjective 
element ;  Matter  is  the  objective  element ;  and  Method  is  the 
process  by  which  these  two  are  linked  together  in  the  attain- 
ment of  educational  results.  The  old  problem  of  common 
school  education  has  been  facetiously  called  the  problem  of 
"the  three  B^s — readin',  'ritin',  and  'rithmetic ; "  the  real 
problem  of  education  ma}^  be  seriously  called  the  problem  of 
the  three  M^s — Man,  Matter,  Method. 

branches  of  Education. — This  analysis  of  the  problem 
of  education  enables  us  to  determine  the  fundamental  branches 
of  the  science  of  education.  Considering  3Ian,  the  first  ele- 
ment of  the  problem,  we  see  that  he  has  susceptibilities  and 
powers  which  may  be  trained  and  developed.  The  process  of 
bringing  forth  these  powers  in  activity,  strength,  and  har- 
mony, we  call  Culture.  This  culture  is  not  a  thing  of 
chance;  there  is  a  proper  way  in  which  it  is  to  be  given. 
The  consideration  of  the  manner  in  which  this  culture  is  to 
be  imparted,  gives  rise  to  the  first  branch  of  the  science 
called  Methods  of  Culture, 

Considering  the  Matter^  the  second  element  of  the  problem, 
we  perceive  that  knowledge,  which  is  a  product  of  the  inind, 
may  be  used  in  giving  culture  to  the  mind.  That  which  came 
forth  from  one  mind  may  be  developed  in  other  minds,  calling 
into  activity  the  faculties  by  which  it  was  originally  produced. 
This  process  of  developing  knowledge  in  the  mind  is  called 
Instruction.  The  consideration  of  the  manner  in  which  in- 
struction may  be  imparted  gives  rise  to  a  second  branch  of 
the  science  called  Methods  of  Instruction. 

At  first  thought,  since  culture  and  instruction  are  seen  to 
embrace  all  possible  educational  processes,  it  would  seem  that 
these  two  branches  constitute  the  entire  science  of  education. 


THE  NATURE   OF   EDUCATION.  15 

A  little  further  analysis,  however,  gives  rise  to  another 
branch  closelj'^  connected  with  these  two  primary  branches, 
and  possibly  contained  in  them,  but  so  important  as  to  be 
regarded  by  some  as  coordinate  with  these  two,  and  requiring 
a  distinct  treatment.  Thus,  since  culture  and  instruction  are 
to  be  given  to  a  number  of  pupils  together,  called  a  school, 
and  this  school  is  to  be  organized,  governed,  etc.,  there  ai'ise 
other  subjects  not  immediately  embraced  in,  or  at  least  not 
conveniently  treated  under,  the  two  primary  branches  of  the 
science.  On  account  of  tlie  intimate  relation  of  these  several 
subjects,  educators  have  treated  them  under  one  head,  and 
regarded  it  as  a  distinct  branch  of  the  science,  which  has  been 
appropriately  named  by  Dr.  Wickorsham,  School  Economy. 

The  science  of  education  is  thus  seen  to  embrace  three 
branches — Methods  of  Culture^  Methods  of  Instruction^  and 
School  Economij.  This  three-fold  division  of  the  science  is 
not  new,  although  it  is  recent.  It  is  not  so  much  of  a  dis- 
covery as  a  growth.  It  seems  to  have  been  gradually  de- 
veloping in  the  minds  of  educators  for  raau}'^  years,  and  is 
now  largely  accepted  by  the  profession  as  a  logical  and  com- 
plete classification. 

Culture  and  Instruction. — Culture  is  the  developing  of  the 
powers  of  man.  It  is  the  art  of  drawing  out  the  different  powers 
and  training  them  so  that  they  may  act  with  skill  and  vigor. 
Instruction  is  the  furnishing  of  the  mind  with  knowledge.  The 
mind  may  be  furnished  with  knowledge  in  two  ways  ;  first  by 
putting  knowledge  into  the  mind,  and  second  by  drawing  know- 
ledge out  of  the  mind.  In  the  fact  studies,  as  history  and  geog- 
laphy,  knowledge  must  be  put  into  the  mind  ;  in  the  thought 
studies,  as  arithmetic  and  grammar,  knowledge  can  be  un- 
folded in  the  mind.  Instruction  is  thus  the  art  of  putting 
knowledge  into  the  mind  and  also  of  drawing  knowledge  out  of 
the  mind.  In  other  words,  instruction  is  the  art  of  developing 
knowledge  in  the  mind,  or  of  building  up  knowledge  in  the  mind. 
These  two  divisions,  Culture  and  Instruction,are  logically  dis- 


]6  METHODS  OF  TEACHING. 

tinguislied.  The  one  seeks  to  draw  out  the  powers  of  the  mind; 
the  other  seeks  to  furnish  the  mind  with  knowledge.  The  for- 
mer is  purely  subjective,  working  from  within  outward ;  the  lat- 
ter is  partly  objective  and  partly  subjective,  as  knowledge  is 
both  put  into  the  mind  and  drawn  out  of  it.  Each,  of  course, 
implies  the  other.  To  give  culture,  we  make  use  of  knowledge ; 
in  imparting  instruction  there  must  be  some  growth  of  the 
mental  powers.  The  two  processes,  however,  are  not  identical ; 
and  the  laws  and  methods  of  each  are  different.  They  are  in 
fact  the  complements  of  each  other  ;  the  two  hemispheres  of 
the  science,  which,  united,  give  it  symmetry  and  completeness. 

Nature  of  Teaching The  act  of  affording  this  culture  and 

imparting  this  knowledge  is  called  Teaching;  and  the  person 
who  does  this  work  is  called  a  Teacher.  The  term  Teaching 
is  also  used  as  the  name  of  the  science  and  art  of  giving  cul- 
ture  and  instruction.  Thus  we  speak  of  the  Science  of  Teach- 
ing and  the  Art  of  Teaching. 

The  term  Teaching,  it  is  thus  seen,  is  a  little  more  compre- 
hensive than  the  word  Instruction.  An  Instructor,  strictly 
speaking,  is  one  who  furnishes  the  mind  with  knowledge ;  a 
Teacher  is  one  wlio  furnishes  the  mind  with  knowledge  and, 
at  the  same  time,  aims  to  give  mental  culture. 

Other  Terms.— The  term  Educator  is  popularly  defined  as 
one  who  educates  or  gives  instruction.  It  is  more  appropri- 
ately used,  however,  to  denote  one  who  is  versed  in,  or  wiio 
advocates  and  promotes,  education.  The  term  Educaiionid 
is  also  employed  in  this  latter  sense,  and  by  many  is  pre- 
ferred to  the  term  Educator. 

The  term  Pedagogics,  or  Pedagogy  (jjais,  paidos,  a  boy, 
and  agogos,  leading  or  guiding),  is  used  by  quite  a  large 
number  of  writers  as  the  name  of  the  science  and  art  of  in- 
struction. The  term  is  popular  in  Germany,  and  efforts  have 
been  made  to  introduce  it  into  this  country  and  England; 
but  so  far  with  but  little  success.  It  is  somewhat  awkward 
and  unmusical,  besides  which,  the  term  pedagogue  is,  in  both 
of  these  countries,  used  as  a  term  of  reproach. 


THE  NATURE   OF   EDUCATION.  17 

The  term  Didactics,  from  didan/co,  I  teach,  is  often  used  as 
the  name  of  the  science  and  art  of  teaching.  The  subject  has 
been  divided  into  two  parts :  General  Didactics,  which 
presents  the  principles  of  teaching  ;  and  Special  Didactics,  or 
Methodics,  which  applies  these  principles  to  the  several 
branches  of  instruction.  The  term  is  appropriate  and  may 
in  time  be  adopted,  but  the  term  Teaching  seems  at  present 
to  be  generall}'  preferred. 

Kinds  of  Education — Education  is  generall}^  divided  into 
Physical  Education,  Intellectual  Education,  and  Moral  and 
Religious  Education.  Phj'sical  Education  is  that  which  per- 
tains to  the  body.  Its  object  is  to  train  every  power  of  the 
body  for  the  attainment  of  the  ends  of  health,  strength,  skill, 
anil  beauty. 

Intellectual  Education  is  that  which  pertains  to  the  intellect. 
Its  object  is  to  develop  all  the  mental  faculties  into  their 
highest  activity,  and  to  furnish  the  mind  with  valuable  and 
interesting  knowledge.  Moral  Education  is  that  which  per- 
tains to  the  moral  nature  of  man.  Its  object  is  the  develop- 
ment of  conscience  and  the  subordination  of  the  will  to  the 
idea  of  duty.  Religious  Education  has  reference  to  the  de- 
velopment of  the  higher  spiritual  instincts  and  sentiments 
forming  the  religious  nature.  It  is  especially  distinguished 
from  moral  education  in  that  the  former  finds  its  motive  in 
human  relations,  and  the  latter  in  the  existence  of  a  Supreme 
Being. 

Besides  these  there  are  also  several  subordinate  or  collateral 
divisions;  as  Esthetic  Education,  which  refers  to  the  culture, 
of  the  imagination  and  taste;  Domestic  Education,  which 
refers  to  the  education  of  children  in  the  household  ;  Common 
School  Education,  which  refers  to  the  education  obtained  in 
a  common  school ;  Popular  Education,  which  refers  to  the 
education  of  the  people  ;  and  National  Education,  which 
refers  to  a  system  of  education  provided  by  the  state. 


CHAPTER  II. 

GENERAL  PRINCIPLES   OF   EDUCATION. 

EDUCATION  is  not  a  matter  of  chance  or  haphazard  pro- 
cedure. All  development  must  proceed  in  accordance 
with  some  regular  plan  or  order.  There  can  be  no  organic 
grow-th  without  the  control  of  principles  determining  and 
shaping  the  development.  The  plant  grows  in  obedience  to 
the  laws  of  vegetable  life ;  and  the  development  of  mind, 
which  is  the  object  of  education,  must  be  controlled  by  the 
laws  of  its  own  being. 

A  system  of  education  must  therefore  be  based  upon 
certain  broad  and  fundamental  principles  which  express  the 
laws  of  human  life  and  development.  These  principles  are 
not  only  the  foundation  upon  which  the  system  rests,  but 
thej^  give  shape  and  character  to  the  entire  superstructure. 
All  the  great  writers  on  education  have  conceived  some  lead 
ins:  ideas  and  endeavored  to  unfold  a  scheme  of  instruction 
growing  out  of  these  fundamental  conceptions. 

From  a  xerj  careful  survey  of  these  different  schemes  and 
a  thorough  examination  of  the  problem  of  education  itself, 
the  following  principles  have  been  reached  which  seem  to 
contain  a  complete  s^'Stem  of  education.  These  principles,  it 
^is  thought,  embrace  all  the  fundamental-  ideas  of  education 
from  Aristotle  to  Pestalozzi  and  Froebel.  The  design  is  to 
enumerate  only  the  general  laws  of  education ;  the  particular 
laws  of  culture  and  instruction  will  be  presented  in  another 
place.  These  principles  are  presented  in  ten  propositions, 
which  we  may  call  our  educational  decalogue. 

1.   The  primary  object  of  education  is  the  perfection  of 
the  individual.     The  educator  should  understand  the  object 

(18) 


GENERAL   PRLN'CIPLES    OF   EDUCATION.  19 

for  which  he  labors;  for  the  object  to  a  large  extent  de- 
termines the  means  and  methods  emploj-ed  in  the  work.  A 
correct  end  in  view  will  lead  to  correct  methods;  a  false  object 
will  vitiate  both  the  means  and  the  methods  of  usins;  them. 
In  education,  especially,  the  end  aimed  at  croMTis  the  work 
with  excellence. 

The  true  object  of  education  has  not  been  generall}'  under- 
stood by  educators  and  parents.  The  ancient  Greeks  made  a 
fundamental  mistake  when  they  based  their  s^'stem  upon  the 
I^erfection  of  the  state  rather  than  the  individual.  Parents 
to-day  send  their  children  to  school  to  fit  them  for  business 
or  a  profession,  to  enable  them  to  make  a  good  living  in  the 
world,  or  to  occupj-  an  honorable  position  in  soeiet}-.  Teachers 
often  seem  to  think  more  about  the  amount  of  knowledge  they 
are  imparting  to  the  child  than  of  the  training  of  its  mind 
and  the  development  of  a  manl}'  and  virtuous  character.  All 
of  these  objects  fall  below  the  high  ideal  we  should  set  before 
us,  and  degrade  and  injure  the  work  of  education. 

We  should,  therefore,  remember  that  the  true  object  of  edu- 
cation is  the  perfection  of  the  individual.  We  should  aim  for 
the  perfecting  of  man  in  his  entire  nature, — physically,  men- 
tally, and  morally.  The  teacher  should  never  forget  that  the 
highest  object  of  his  work  is  the  fullest  and  most  complete 
development  of  the  immortal  beings  committed  to  his  care : 
and  that  his  work  is  not  onlj'  for  time  but  for  eternitj-.  In 
other  words,  it  should  be  remembered  that  the  highest  object 
of  education  is  human  perfection. 

2.  The  perfection  of  the  individual  is  attaitied  by  a  har 
monious  development  of  all  his  powers.  Man  possesses  a 
multiplicity  of  capacities  and  powers,  all  of  which  contribute 
to  his  well-being  and  his  dignity.  A  perfectly'  developed  man- 
hood or  womanhood  implies  the  complete  development  of 
every  capacity  and  gift.  These  powers  are  so  related  that 
they  may  be  unfolded  in  very  nearly'  equal  proportions,  and 
harmoniously  blend  in  the  final  result.     For  the  attainment 


20  METHODS   OF   TEACHING. 

of  our  ideal  such  a  development  is  required.  The  educational 
work  should  reach  ever}^  power,  and  aim  at  a  full  and  har- 
monious development  of  them  all. 

This  principle  is  limited  by  the  existence  of  special  talents 
and  the  demand  for  special  duties.  While  a  general  scheme 
of  education  should  seek  to  give  culture  to  all  the  powers,  we 
should  not  be  neglectful  of  special  and  unusual  gifts.  Genius 
should  be  recognized,  and  our  general  system  be  so  far  modi- 
fied as  to  give  opportunity  for  its  highest  development  and 
achievements.  An  unusual  gift  for  poetry,  music,  painting, 
mechanics,  mathematics,  etc.,  should  be  recognized,  and  oppor- 
tunity offered  for  its  fullest  development. 

We  must  remember  also  that  duties  are  diverse  as  well  as 
talents,  and  that  special  training  is  needed  for  the  preparation 
of  mankind  to  discharge  these  special  duties.  There  must 
be  farmers,  and  artisans,  and  physicians,  etc.,  and  they  need 
special  preparation  for  their  work ;  and  educational  systems 
must  recognize  this  fact  and  provide  for  it. 

The  principle  of  harmonious  development  has  reference  to 
that  general  educational  preparation  which  all  persons  need 
for  their  own  personal  excellence,  and  as  a  preparation  for  a 
special  course  of  instruction  to  prepare  them  for  specific 
duties  and  occupations.  The  general  scheme  of  education 
should  therefore  aim  at  a  full  and  harmonious  development  of 
all  of  man's  powers. 

3.  These  poivers  develop  naturally  in  a  certain  order,  which 
should  be  followed  in  education.  Intellectual  life  seems  to 
begin  in  the  senses ;  the  child  awakens  into  knowledge  through 
sensation  and  perception.  Then  follows  the  action  of  the 
memory  as  a  retaining  and  a  recalling  power,  accompanied 
by  imagination  as  the  power  of  representation.  After  this 
come  judgment  and  reasoning  and  the  power  of  abstraction, 
seneralization,  and  classification.  Still  later  we  become  con- 
scions  of  the  intuitive  ideas  and  truths,  and  learn  to  work 
them  up  into  new  truths  by  the  power  of  deductive  thought. 


GENERAL  PRINCIPLES   OF   EDUCATION.  21 

Last  of  all,  the  mind  awakens  to  the  consciousness  of  man  aa 
a  moral  and  religious  being,  bearing  relations  to  his  fellow 
man  and  to  God. 

Finding  in  man  such  a  relation  of  faculties  and  powers,  we 
should  learn  the  order  of  their  development  and  follow  that 
order  in  our  work.  TVe  should  first  afford  food  for  the  growth 
of  the  mind  through  the  senses.  We  should  call  the  memory 
into  activity,  and  afford  means  for  the  culture  of  the  imagina- 
tion. We  should  lead  the  mind  gradually  from  things  to 
thoughts,  and  give  activit}'  to  judgment  and  reasoning,  and 
also  to  the  powers  of  abstraction  and  generalization.  Desires 
should  be  awakened  and  directed,  the  affections  unfolded,  and 
the  will  be  subordinated  to  the  ideas  of  truth  and  duty 

Though  these  powers  develop  in  a  certain  order,  it  is  not 
to  be  thought  that  the  activity  of  one  waits  upon  the  full 
development  of  another.  To  a  certain  extent  they  are  all 
active  at  the  same  time  ;  but  they  are  active  in  different  de- 
grees. The  order  given  represents  the  relative  activity,  and 
thus  indicates  the  relative  attention  required  to  be  given  them 
in  the  work  of  education.  Such  a  relation  should  be  clearly 
understood  by  the  educator,  and  should  guide  him  in  his  work. 

4.  The  basis  of  this  development  is  the  self-activity  of  the 
child.  Education  is  a  spiritual  growth,  and  not  an  accre- 
tion. It  is  a  development  from  within,  and  not  an  aggrega- 
tion from  without.  For  this  growth  there  must  be  forces 
working  within  the  child.  This  force  is  the  self-activity  of 
the  soul,  going  out  towards  an  object  as  well  as  receiving 
impressions  from  it ;  gaining  power  in  the  effort,  and  work- 
ing up  into  organic  products  the  knowledge  thus  acquired. 

The  object  of  education  is  to  stimulate  and  direct  this 
natural  activity.  The  teacher,  therefore,  should  never  do  for 
the  child  what  it  can  do  for  itself.  It  is  the  child's  own 
activity  that  will  give  strength  to  its  powers  and  increase  the 
capacity  of  the  mind.  The  teacher  must  avoid  telling  too 
much,  or  aiding  the  child  too  frequently.     A   mere  hint  or 


22  "METHODS   OF   TEACHING. 

suggestive  question  to  lead  the  mind  in  the  proper  direction 
is  worth  much  more  than  direct  assistance,  for  it  not  only 
gives  activity'  and  consequently  mental  development,  but  it 
cultivates  the  power  of  original  investigation. 

We  should  aim  to  cultivate  a  taste  and  desire  for  knowledge 
on  the  part  of  the  child,  so  that  this  activity  may  be  natural 
and  healthful.  To  force  the  mind  to  the  reception  of  knowl- 
edge is  not  education,  it  is  cramming  ;  and  tlie  object  of  educa- 
tion is  not  cram  but  culture.  For  the  attainment  of  the  high 
end  of  education,  therefore,  we  must  depend  on  the  self- 
activity  of  the  child ;  and  it  is  the  teacher's  office  to  excite 
and  direct  this  activity. 

5.  This  self-activity  has  two  distinct  phases;  from  without 
inward^ — receptive  and  acquisitive;  and  from  within  out- 
ward^— productive  and  expressive.  First,  the  mind  is  re- 
ceptive of  knowledge.  Objects  of  the  material  world  make 
their  impressions  upon  the  senses,  and  ideas  and  thoughts 
spring  up  in  the  mind.  Knowledge  thus  comes  into  the  mind 
from  without  through  the  senses.  The  contents  of  books  also 
flow  into  the  mind  through  written  language,  and  are  treas- 
ured in  the  memory.  In  all  this  the  mind  is  receptive,  the 
process  is  from  without  inward,  and  the  result  is  acquisition, 
learning. 

The  mind  is  also  active  in  creating  as  well  as  in  receiving. 
It  has  the  power  to  reproduce  as  well  as  to  receive.  In  its 
self-activity  it  can  take  the  material  thus  acquired,  and  work 
it  up  into  new  products.  It  can  also  send  it  forth  on  the 
stream  of  clear  and  definite  expression  in  audible  or  visible 
speech.  It  thus  works  from  within  outward,  creating,  and 
evolving  what  it  creates. 

The  mind  in  its  receptive  phase  is  said  to  be  intuitive; 
that  is,  the  knowledge  comes  directlv  into  the  mind.  The 
mind  in  the  second  phase  is  called  elaborative,  because  it 
works  up  the  material  into  new  products.  This  distinction 
has  also  an  educational  significance. 


GENERAL   PRINCIPLES    OF    EDUCATION.  23 

6.  These  two  phases,  the  receptive  and  productive,  should 
go  hand  in  hand  in  the  work  of  education.  This  is  evident 
from  their  natural  correlation.  The  activity  of  the  mind  in 
receiving  naturally  creates  the  correlative  activitT^  of  produc- 
ing. The  knowledge  coming  into  the  mind  through  the  re- 
ceptive capacity  excites  the  mind  to  a  productive  activity. 
It  acts  like  food  in  the  stomach,  which  excites  the  powers  of 
digestion  and  assimilation.  Besides,  the  knowledge  gained 
by  the  receptive  powers  becomes  the  material  for  the  produc- 
tion of  the  creative  powers.  This  material  is  operated  upon 
and  worked  up  into  new  products. 

These  two  operations  are  not  to  be  separated  in  education. 
Each  gives  life  and  vigor  to  the  other.  The  receptive  powers 
are  stimulated  by  the  activity  of  the  productive  powers,  and 
the  productive  powers  are  set  into  immediate  activity  by  the 
presence  of  receptive  knowledge.  They  thus  play  into  each 
other's  hands,  act  as  a  mutual  stimulus  to  each  other,  and 
should  go  hand  in  hand  in  the  work  of  education. 

7.  There  must  be  objective  realities  to  supply  the  condition 
for  the  self-activity  of  the  mind.  The  mind  cannot  act  upon 
itself  alone ;  there  must  be  food  for  the  mental  appetite.  There 
must  be  an  external  world  of  knowledge  to  meet  the  wants  ol 
the  internal  knowing  subject. 

Such  an  external  world  is  supplied.  There  is  a  world  of 
knowledge  suited  to  and  correlating  with  the  wants  of  the  soul. 
The  objective  world  of  nature  is  found  to  be  an  embodiment 
of  thought,  and  this  thought  developed  into  science  meets  the 
wants  of  the  active  spirit.  There  is  also  the  great  world  of 
space  and  number,  with  its  ideas  and  truths ;  and  also  the 
loftier  abstractions  of  the  True,  the  Beautiful,  and  the  Good. 

This  world  of  knowledge  is  adapted  to  every  power  and 
capacity  of  the  mind.  This  is  evident,  since  knowledge  is  the 
product  of  the  mind  operating  upon  external  realities.  Knowl- 
edge as  the  product  of  one  mind  must  be  suited  to  the  differ- 
ent capacities  of  all  other  minds.     It  is  thus  seen  that,  there 


24  METHODS   OF   TEACHINQ. 

is  abundant  provision  for  the  activity  and  growth  of  all  of 
the  powers  of  the  mind. 

8.  Education  is  not  creative ;  it  only  assists  in  developing 
existing  possibilities  into  realities.  The  mind  possesses  in- 
nate powers.  These  may  be  awakened  into  a  natural  activity. 
The  desisrn  of  education  is  to  aid  nature  in  unfolding  the 
powers  she  has  given.  No  new  power  can  be  created  hy  edu- 
cation; the  object  is  to  arouse  those  which  exist  to  a  health- 
ful activity,  and  to  guide  them  in  their  unfolding.  In  other 
words,  the  object  of  education  is  to  aid  nature  in  unfolding 
the  possibilities  of  the  child  into  the  highest  possible  realities. 

9.  Education  should  be  modified  by  the  different  tastes  and 
talents  of  the  pupil.  All  minds  possess  the  same  general 
capacities  or  powers.  These  powers  are,  however,  possessed 
in  different  degrees.  An  unusual  gift  of  any  one  or  more 
powers  constitutes  genius.  Tastes  or  dispositions  for  par- 
ticular branches  of  science  or  art  also  differ. 

Such  differences  should  not  be  overlooked  in  a  scheme  of 
education.  While  all  should  receive  a  course  of  general  cul- 
ture, opportunity  should  be  given  for  the  development  of 
special  tastes  and  gifts.  It  is  these  which  enrich  science  and 
art,  and  add  to  the  sum  of  human  knowledge ;  and  the  pro- 
gress of  science  and  art  demands  that  genius  shall  have  the 
most  abundant  opportunities  for  its  fullest  and  highest  devel- 
opment. 

10.  A  scheme  of  education  should  aim  to  attain  the  triune 
results — development,  learning,  and  efficiency.  Development 
relates  to  the  culture  and  growth  of  the  powers  of  the  child. 
This  is  the  fundamental  idea  of  education,  and  is  of  primary 
importance.  Education  has  reference  also  to  the  acquisition 
of  knowledge.  It  aims  to  enrich  the  mind  with  the  truths  of 
science,  to  make  a  man  learned,  to  produce  scholars. 

A  third  object  is  the  acquisition  of  skill  in  the  use  of  culture 
and  knowledge.  It  is  not  enough  that  the  mind  has  well-devel- 
oped powers  and  is  richly  furnished  with  knowledge.     There 


GENERAL   PRINCIPLES   OF   EDUCATION.  25 

should  be  the  power  to  make  use  of  this  culture  and  knowl- 
edge. The  educated  man  should  be  able  to  do  as  well  as  to 
think  and  know.  This  third  design  of  the  educator,  the  attain- 
ment of  skill,  should  not  therefore  be  overlooked.  The  true 
aim  of  education  is  thus  seen  to  be  the  attainment  of  the  three 
ends — culture,  knowledge,  and  efficiency. 
8 


CHAPTER  III. 

THE    SCIENCE    OF   TEACHING, 

TEACHING,  as  a  science,  treats  of  the  Laws  and  Methods 
of  human  Culture  and  Instruction.  The  terra  is  derived 
from  the  Saxon  word  tcecan,  which  meant  to  show,  to  teach, 
and  is  allied  to  the  Greek  deiknunai^  to  show,  and  the  Latin 
docere,  to  teach. 

Primarily,  the  word  appears  to  have  meant  very  nearly  the 
same  as  the  word  instruction ;  though  even  in  its  primary  sense 
of  directing  or  showing,  it  is  suggestive  of  the  act  of  develop- 
ing the  mind  as  well  as  instructing  it.  At  the  present  daj''. 
Teaching  embraces  both  Culture  and  Instruction, — the  bring- 
ing out  and  training  of  the  powers,  as  well  as  the  furnishing 
or  the  mind  with  knowledge.  A  true  teacher  seeks  to  culti- 
vate the  minds  of  his  pupils  as  well  as  to  instruct  them. 

Laivs  and  Methods. — The  definition  of  Teaching  embraces 
four  distinct  and  prominent  ideas, — Laws,  Methods,  Culture, 
and  Instruction.  Bv  Laws  we  mean  the  principles  that  guide 
us  in  an  operation.  Thus,  in  grammar,  the  principle  that  the 
verb  agrees  with  its  subject  in  number  and  person,  will  guide 
us  in  speaking  and  writing  correctl}'.  So  the  principles  of 
numV)ers  enable  us  to  operate  with  them  correctly  in  applying 
them  to  the  business  transactions  of  life. 

B}'  Methods  we  mean  the  manner  of  performing  an  opera- 
tion. Thus,  in  arithmetic  we  have  the  methods  of  subtracting, 
of  finding  the  greatest  common  divisor,  etc.  The  rules  of 
arithmetic  are  statements  of  methods  of  operation.  So  also 
in  education,  there  are  methods  of  doing  things  or  of  obtaining 
certain  results.  There  are  methods  of  giving  culture  to  the 
dilferent  faculties,  and  also  of  teaching  the  dillerent  branches. 

(26; 


THE   SCIENCE    OF  TEACHING.  27 

The  relation  of  Laws  and  Methods  should  be  clearl}^  under- 
stood. Principles  are  self-existent,  or  belong  to  the  very  na- 
ture of  the  subjects  ;  Methods  are  derived  from  principles  ; 
they  are  the  outgrowth  of  laws  or  principles.  Principles  are 
of  more  value  than  methods ;  if  you  know  the  principle,  you 
can  derive  the  method,  though  you  may  know  the  method 
without  understanding  the  principle.  One  who  is  familiar 
with  principles  is  thus  much  more  independent  than  one  who 
knows  only  methods.  These  relations  of  principles  and 
methods  may  be  illustrated  in  arithmetic  and  grammar,  and 
in  other  school  studies. 

Cultiir'e  and  Instruction. — Culture  is  the  developing  of 
the  powers  of  man.  The  term  is  derived  from  colo,  I  culti- 
vate, and  derives  its  educational  meaning  from  the  act  of  tilling 
and  enriching  the  soil.  It  has  reference  to  the  deA'^elopment 
and  improvement  of  any  of  man's  faculties  or  powers.  To 
awaken  the  mind  into  activity,  to  call  out  and  mould  its  vari- 
ous faculties,  to  train  the  e3'e  to  see,  the  memory  to  retain 
and  recall,  the  understanding  to  think  and  reason,  etc,— this 
is  to  cultivate  the  mind. 

Instruction  is  the  furnishing  of  the  mind  with  knowledge. 
It  is  the  process  of  developing  knowledge  in  the  mind  of  an- 
other. The  term  is  derived  from  i?i,  into,  and  atruo^  I  build, 
meaning,  I  build  into.  To  instruct  the  mind  is  thus  to  furnish 
it  with  knowledge,  to  build  up  knowledge  in  the  mind.  The 
instructor  takes  the  knowledge  that  is  in  his  own  mind,  and 
puts  it  into  the  minds  of  his  pupils  ;  or  he  dcA'elops  knowledge 
in  the  minds  of  his  pupils,  and  builds  it  up  there,  as  an  archi- 
tect erects  a  temple,  in  symmetry  and  proportion. 

The  relation  of  Culture  and  Instruction  should  be  clearly 
understood.  The  object  of  Culture  is  to  strengthen  and  de- 
velop the  mind  ;  the  object  of  Instruction  is  to  furnish  the  mind 
with  knowledge.  Culture  gives  a  person  mental  power ;  Instruc- 
tion gives  him  information  or  learning.  They  are  both  impor- 
t:iut ;  but  Culture  is  more  important  than  mere  Instruction. 


28  METHODS  OF   TEACHING. 

To  be  able  to  acquire  knowledge  is  worth  more  than  the  knowl 
edge  we  have  acquired.  The  ability  to  originate  knowledge  is 
even  more  important.  A  person  should  know  more  than  he 
ever  learned ;  and  this  is  possible  when  his  powers  have  been 
cultivated.  The  object  of  the  teacher,  therefore,  should  be  not 
merely  to  impart  knowledge,  but  to  cultivate  mental  power. 

Teachbiff  a  Scieiice. — Teaching  is  both  a  science  and  an 
art.  That  it  is  a  science,  which  has  l)«.'cn  questioned,  will 
appear  from  the  following  considerations:  To  constitute  a  sci- 
ence we  must  have  three  things:  1.  Knowledge;  2.  Knowl- 
edge sj'stematized ;  3.  Principles  showing  the  relations  of  this 
knowledge,  and  binding  it  together  into  an  organic  unity. 
There  is  a  knowledge  of  teaching,  as  is  attested  by  the  many 
works  and  articles  written  upon  the  subject.  This  knowledge 
can  be  S3^stematized  as  logically  as  the  knowledge  of  grammar 
or  arithmetic.  There  are  also  fundamental  principles  of  teach- 
ing, which  express  the  laws  of  culture  and  instruction.  Hence, 
from  the  delinition  of  a  science,  we  can  claim  that  there  is  a 
science  of  teaching. 

Branches  of  Teaching. — The  Science  of  Teaching  is 
divided  into  three  branches  ;  llethods  of  Culture,  Methods  of 
Instruction,  and  School  Economy.  This  three-fold  division 
embraces  everything  that  pertains  to  teaching,  and  is  therefore 
regarded  as  exhaustive.  Indeed,  as  previously  stated,  since 
man  can  only  be  cultured  and  instructed,  it  would  seem  that 
there  could  be  only  two  distinct  branches.  Methods  of  Cul- 
ture and  Methods  of  Instruction ;  but  since  this  work  is  to  be 
done  with  the  pupils  organized  into  a  school,  and  since  such 
an  organization  gives  rise  to  special  regulations  and  provis- 
ions, there  incidentally  arises  a  third  division,  called  School 
Economy. 

Methods  of  Culture  treats  of  the  nature  of  the  powers  of 
man,  and  how  to  develop  them.  It  embraces  three  general 
divisions:  1.  The  Nature  of  Man;  2.  The  Nature  of  Culture; 
3.  The  Methods  of  Cultivating  each  Faculty.     In  a  ftdl  treat- 


THK    SCIENCE    OF   TEACHING.  29 

ise  upon  this  subject,  each  one  of  these  topics  should  be  dis- 
cussed in  detail. 

Methods  of  Instruction  treats  of  the  different  branches  of 
knowledge  and  how  to  teach  them.  It  embraces  three  general 
divisions:  1.  The  Nature  of  Knowledge;  2.  The  Nature  of 
Instruction;  3.  The  Methods  of  Teaching  each  Branch.  In  a 
full  treatise  upon  the  subject,  each  one  of  these  topics  should 
he  discussed  in  detail. 

The  three  divisions  of  these  two  branches  of  Teaching,  are 
seen  to  correlate.  Thus  the  Nature  of  Man  in  the  first  branch 
correlates  with  the  Nature  of  Knowledge  in  the  second ;  the 
Nature  of  Culture  in  the  former  corresponds  to  the  Nature  of 
Instruction  in  the  latter;  and  the  Method  of  Cultivating  each 
Power  is  correlative  with  the  Method  of  Teaching  each 
Branch.  As  the  two  branches  stand  in  the  relation  of  the 
subjective  and  the  objective,  so  do  the  corresponding  divi- 
sions of  the  two  branches. 

School  Economy  treats  of  the  methods  of  organizing  and 
managing  a  school.  It  embraces  five  things:  1.  School  Pre- 
paration; 2.  School  Organization;  3.  School  Employments; 
4.  School  Government ;  5.  School  Authorities.  This  classifi- 
cation is  that  presented  by  Dr.  Wickersham,  and  is  regarded 
as  logical  and  complete. 

The  relation  of  the  several  branches  of  the  Science  of  Teach- 
ing, together  with  a  few  of  their  practical  divisions,  is  expressed 
in  the  following  outline : 

{Nature  of  Man. 
Nature  of  Culture. 
Method  of  Cultivating  each  Faculty. 

(Nature  of  Knowledge. 
Nature  of  Instruction. 
Method  of  Teaching  each  Branch. 

School  Preparation. 
School  Organization. 
School  Employments. 
School  Government. 
School  Authorities. 


12; 


S5 


a:  o  o 


3.  School  Economy. 


30  METHODS    OF   TEACHING. 

In  this  work  we  design  to  speak  mainly  of  Methods  of 
Instruction,  but  so  necessary  is  a  knowledge  of  the  mind  and 
the  methods  of  training  it  that  we  shall  give  a  single  chapter 
to  each  of  the  three  divisions  of  Methods  of  Culture;  namely, 
The  Nature  of  Mind,  the  Nature  of  Culture,  and  the  Methods 
of  Cultivating  each  Faculty.  We  shall  then  speak  of  the 
Nature  of  Knowledge  and  the  Nature  of  Instruction,  embrac- 
ing under  the  latter  head,  Forms  of  Instruction,  Order  of 
Instruction,  and  Principles  of  Instruction.  Having  laid  this 
foundation,  we  shall  proceed  to  the  consideration  of  the 
Methods  of  Teaching  each  Branch  of  Knowledge. 


CHAPTER  IV. 

THE   NATLTRE    OF   THE    MIND. 

THE  Mind  is  that  which  thinks,  feels,  and  wills.  It  is  that 
immaterial  principle  which  we  call  the  soul,  the  s^'irit, 
or  the  intelligence.  Of  its  essence  or  substance,  nothing  is 
known ;  we  know  it  only  b}'  its  activities  and  its  operations. 
The  ditferent  forms  of  activity  which  it  presents,  indicate 
diJferent  mental  powers,  which  are  called  Faculties  of  the 
mind. 

A  Mental  Facixtt  is  a  capacity  for  a  distinct  form  of 
mental  activity.  It  is  ilie  mind's  power  of  doing  something, 
of  putting  forth  some  energy,  of  manifesting  itself  in  some 
particular  manner.  The  mind  possesses  as  many  faculties  as 
there  are  distinct  forms  of  mental  activity.  In  order,  there- 
fore, to  ascertain  the  different  faculties  of  the  mind,  we  must 
notice  carefully  the  various  ways  in  which  the  mind  acts. 

General  Classification. — The  mind  embraces  three  general 
classes  of  faculties ;  the  Intellect.,  the  Sensibilities,  and  the 
Will.  Every  capacity  or  power  which  the  mind  possesses  falls 
under  one  of  these  three  heads.  Every  mental  act  is  an  act  of 
the  Intellect,  the  Sensibilities,  or  the  Will. 

This  three-fold  division  of  the  mind  is  the  latest  teaching  of 
philosophy.  These  three  classes  of  faculties  are  not  to  be  consid- 
ered, however,  as  parts  of  a  complex  unit,  but  rather  as  forms  of 
manifestation  of  the  spiritual  entity  which  we  call  The  3Iincl. 
The  mind  is  thus  a  tri-unity, — one  substance  with  a  trinity  of 
powers  or  capacities.  The  doctrine  of  the  Trinity  of  the  Mind  is 
thus  a  fundamental  fact  of  Psychology. 

The  Intellect  is  the  power  by  which  we  think  and  know. 
Its  products  are  ideas  and  thoughts.     An  Idea  is  a  mental  pro- 

(31) 


82  METHODS   OF    TEACHING. 

duct  which  may  be  expressed  in  one  or  more  wf)rds,  not  forming 
a  proj)Ositi<)n  ;  a^,  a  man,  an  aiiimu/,  etc.  A  Thouirht  is  a  mental 
product  consisting  of  the  combination  of  two  or  more  ideas,  which 
when  expressed  in  words,  gives  us  a  proposition ;  as,  a  man  is  an 
animal. 

The  Sensibilities  are  the  powers  by  which  we  feel.  Their 
products  are  emotions^  affections^  and  desires.  An  emotion  is 
a  simjde  feeling,  as  the  emotion  of  joy,  sorrow,  etc.  An  affec- 
tion is  an  emotion  that  goes  out  towards  an  object ;  as  love, 
hate,  envy,  etc.  A  denire  is  an  emotion  that  goes  out  to  an 
object  with  the  wish  of  possession ;  as  the  desii'e  of  wealth, 
fame,  etc. 

The  Will  is  the  power  by  w^hich  we  resolve  to  do.  It  is 
the  executive  power  of  tlie  mind,  the  power  by  which  man 
becomes  the  conscious  autlior  of  an  intentional  act.  The 
products  of  the  Will  are  volitiotis  and  voluntary  actions.  It  is 
in  the  domain  of  the  Will  that  man  becomes  a  moral  and 
responsible  being. 

The  relation  of  these  three  spheres  of  activity  may  be  illus- 
trated in  a  variety  of  ways.  I  read  of  the  destitution  and 
suffering  in  a  great  city  and  understand  the  means  taken  for 
their  relief;  this  is  an  act  of  the  intellect.  I  feel  a  deep  sym- 
pathy with  this  suffering ;  my  heart  is  touched  with  pity,  and 
I  experience  a  strong  desire  to  aid  in  relieving  their  distress; 
this  is  an  act  of  the  sensibilities.  I  desire  to  express  my 
feelings  of  pity  and  follow  my  sense  of  duty,  and  resolve  to 
aid  them  by  sending  a  contribution  or  going  personally  to 
their  relief;  this  is  an  act  of  the  will. 

The  Intellect. — The  Intellect  embraces  several  distinct 
faculties;  Perception,  Memory,  Imagination,  Understanding, 
and  Intuition,  or  the  Reason.  This  classification  of  the  Intel- 
lect is  how  almost  universally  accepted,  though  writers  occa- 
sionally differ  in  the  terms  they  use  to  name  the  different 
powers. 

Perception  is  the  power  by  which  we  gain  a  knowledge  of 


NATURE    OF    THE    MESTD.  33 

external  objects  through  the  senses.  It  is  the  faculty  b}^  which 
we  gain  a  knowledge  of  objects  and  their  qualities.  Its  pro- 
ducts are  ideas  of  external  objects  and  of  the  qualities  of  ob- 
jects. The  ideas  which  we  possess  of  persons,  places,  things, 
etc.,  are  mainly  given  b)^  perception. 

Memoky  is  the  power  by  which  we  retain  and  recall  knowl- 
edge. It  enables  us  to  hold  fast  to  the  knowledge  we  have 
acquired,  and  also  to  recall  it  when  we  wish  to  u?e  it.  These 
two  offices  of  the  Memory  are  distinguished  as  lietention  and 
Recollection.  By  some  writers  these  are  regarded  as  separate 
faculties;  and  others  again  discard  the  element  of  retention. 
Besides  these,  the  memory  also  gives  us  a  representation  of 
that  which  it  recalls,  and  recognizes  it  as  something  of  our 
past  experience. 

Imagination  is  the  power  by  which  we  form  ideal  concep- 
tions. It  is  the  power  of  forming  mental  images  by  uniting 
different  parts  of  objects  given  by  perception,  and  also  of 
creating  ideals  of  objects  different  from  an3'thing  we  have  per- 
ceived. Thus,  I  can  conceive  oi  a,  flying  horse  by  uniting  my 
ideas  of  wings  and  a  horse ;  or  I  can  imagine  a  landscape  or 
a  strain  of  music  different  from  anything  I  have  ever  seen  or 
heard.     Imagination  is  thus  the  power  of  ideal  creation. 

The  Undebstandinq  is  the  power  by  which  we  compare  ob- 
jects of  thought  and  derive  abstract  and  general  ideas  and 
truths.  It  is  the  elaborative  power  of  the  mind;  it  takes 
the  materials  furnished  by  the  other  faculties  and  works  them 
up  into  new  products.  Its  products  are  abstract  and  general 
ideas,  truths,  laws,  causes,  etc. 

Intuition,  or  the  Reason,  is  the  power  which  gives  us  ideas 
and  thoughts  not  furnished  by  the  senses  nor  elaborated  by 
the  Understanding.  Its  products  are  called  primary  ideas 
and  primary  truths.  The  Primary  Ideas  are  such  as  Space, 
Time,  Cause,  Identity,  the  True,  the  Beautiful,  and  the  Good. 
The  Primary  Truths  are  all  self-evident  truths,  as  the  axioms 
of  mathematics  and  logic. 
2* 


S4  METHODS   OF   TEACHING. 

The  Understanding. — The  Understanding  embraces  sev- 
eral distinct  faculties  or  forms  of  mental  activity.  These  are 
Abstraciicn,  Conception,  Judgment,  and  Reasoning.  This 
division  is  now  almost  universally  adopted,  and  the  same 
terms  are  employed  by  nearly  all  modern  -writers. 

Abstraction  is  the  power  of  forming  abstract  ideas.  It  is 
the  power  by  which  the  mind  draws  a  quality  away  from  its 
object,  and  makes  of  it  a  distinct  object  of  thought.  Its  pro- 
ducts are  abstract  ideas,  such  as  hardness,  softness,  color,  etc. 
The  naming  of  abstract  ideas  gives  us  abstract  terms.  The 
term  Abstraction  is  derived  from  ab,  from,  and  traho,  I  draw, 
and  signifies  a  drawing  from. 

Conception  is  the  power  of  forming  general  ideas.  By  it 
we  take  several  particular  ideas,  and  unite  their  common  prop- 
erties, and  thus  form  a  general  idea  which  embraces  them  all. 
The  products  of  Conception  are  general  ideas,  or  ideas  of 
classes;  as  horse,  bird,  man,  etc.  The  naming  of  general 
ideas  gives  us  common  terms.  This  faculty  is  often  called 
generalization ;  but  the  term  Conception  is  more  appropriate, 
and  is  the  one  generallj-  adopted  by  logicians.  The  term 
Conception  is  derived  from  con,  together,  and  cajno,  I  take ; 
and  signifies  a  taking  together. 

Judgment  is  the  power  of  perceiving  the  agreement  or  disa- 
greement of  two  objects  of  thought.  It  is  the  power  of  com- 
parison. It  compares  one  object  directly  with  another,  and 
gives  us  a  proposition.  A  proposition  is  a  judgment  ex- 
j tressed  in  words.  Thus,  a  bird  is  an  animal,  is  a  judgment 
expressed.  The  term  Judgment  is  applied  to  both  the  mental 
facult}^  and  its  product. 

Reasoning  is  the  power  of  comparing  two  ideas  through 
their  relation  to  a  third.  It  is  a  process  of  indirect  or  medi- 
ate comparison.  It  deals  with  three  objects  of  thought  and 
requires  three  propositions.  Thus,  suppose  I  wish  to  com- 
pare A  and  B,  and  perceiving  no  relation  between  them,  see 
that  A  equals  C,  aad  B  equals  C,  and  thus  infer  that  A  equals 
B ;  such  an  inference  is  an  act  of  reasoning. 


NATURE    OF    THE    MIND.  35 

The  form  in  which  reasoning  is  expressed  is  called  a  Syllih 
yism.  A  Sj'Ilogism  consists  of  three  propositions  so  related 
that  one  of  them  is  an  inference  from  the  other  two.  Two  of 
these  propositions  are  called  the  i^remises  and  the  third  the 
conclusion.  Thus,  in  the  above  example  the  two  propositions, 
"A  equals  C"  and  "B  equals  C,"  are  the  premises;  and  "A 
equals  B"  is  the  conclusion. 

Reasoning  is  of  two  kinds;  Inductive  Seasoning  and  De- 
ductive Reasoning.  Inductive  Reasoning  is  the  process  of 
deriving  a  general  truth  from  particular  truths.  Thus,  if  I 
find  that  heat  expands  several  metals,  as  zinc,  iron,  copper, 
etc,  I  may  infer  that  heat  will  expand  all  metals.  Such  an 
inference  of  a  general  truth  from  the  particular  facts  is  called 
Induction.  Inductive  Reasoning  proceeds  upon  the  principle 
that  ichat  is  true  of  the  many  is  true  of  the  whole. 

Deductive  Reasoning  is  the  process  of  deriving  a  particu- 
lar truth  from  a  general  truth.  Thus,  from  the  general  propo- 
sition that  heat  expands  all  metals,  I  may  infer  by  Deduction 
that  heat  will  expand  any  particular  metal,  as  silver.  Deduc- 
tion proceeds  upon  the  principle  that  what  is  true  of  the  whole 
is  true  of  the  parts. 

Other  Forms  of  Mental  Activity. — Besides  the  faculties 
now  named,  there  are  two  other  forms  of  mental  activity,  or 
mental  states,  called  Consciousness  and  Attention.  These  are 
not  regarded  as  specific  faculties  of  the  mind,  but  as  condi- 
tions or  accompaniments  of  these  faculties. 

Cotisciousness. — Consciousness  is  the  power  or  attribute  of 
the  mind  by  which  it  knows  its  own  states  or  actions.  The 
term  is  derived  from  con,  with,  and  scio,  I  know,  and  means  a 
knowing  with  the  mental  acts  or  states.  It  is  regarded  as  an 
attribute  of  the  mind,  involved  in  the  very  idea  of  mind,  and 
not  as  a  mental  faculty.  Thus,  to  know  is  to  know  we  know, 
to  feel  is  to  know  we  feel,  to  will  is  to  know  we  will.  The 
expressions,  "I  know  that  I  know,"  "I  know  that  I  feel," 
etc.,  are  equivalent  to  I  am  conscious  that  1  know,  I  am  con- 


S6  METHODS    OF   TEACHING. 

scious  that  I  feel,  etc.  Coiisciousness  is  a  kind  of  inner  light 
by  which  one  knows  what  is  going  on  within  his  mind  ;  it  is  a 
revealer  jf  the  internal  phenomena  of  thought,  feeling,  and 
will. 

Atteiition. — Attention  is  the  power  of  directing  the  mind 
voluntarily  to  any  object  of  thought  to  the  exclusion  of 
others.  It  is  the  power  of  selecting  one  of  several  objects, 
and  concentrating  the  mental  energies  upon  it.  The  term  is 
derived  from  ac^,to,  and  tendo^  I  bend,  which  was  probal  ly 
suggested  by  the  attitude  of  the  body  in  listening  attentively 
to  a  sound. 

Attention  is  not  a  distinct  form  of  mental  activity,  but  is 
involved  in  and  underlies  the  activity  of  all  the  faculties. 
The  voluntary  operation  of  any  of  the  mental  powers,  as  Per- 
ception, Memorj^,  etc.,  carries  with  it  an  act  of  attention.  It 
is  not  the  power  of  knowing,  but  of  directing  that  which  ma;' 
know.  It  has  no  distinct  field  or  province  of  its  own,  yet, 
without  it  the  faculties  would  be  of  little  use  to  us.  It  works 
with  them  and  through  them,  increasing  their  efficiency,  and 
giving  them  a  power  they  would  not  otherwise  possess. 

Conception. — The  term  Conception  is  often  used  in  a  gen- 
eral and  popular  sense,  meaning  that  power  which  the  mind 
has  of  making  anything  a  distinct  object  of  thought.  In  this 
sense  it  is  intimately  related  to  all  the  mental  faculties.  Thus 
I  can  conceive  of  a  tree  or  a  horse  which  I  have  seen,  a  land- 
scape which  I  may  not  have  seen,  a  proposition  in  geometry, 
a  truth  in  natural  philosophy,  etc.  Some  writers  have  used 
the  term  in  a  more  specific  sense,  as  the  power  of  forming  an 
exact  transcript  of  a  past  perception.  In  Logic  the  term  is 
restricted  to  the  power  of  forming  general  ideas,  as  we  have 
previously  defined  it. 


CHAPTER   V. 

THE   NATURE    OF    CULTURE. 

CULTURE,  as  alread\^  defined,  is  the  developing  of  the 
powers  of  man.  It  aims  at  the  unfolding  and  growth  of 
all  the  powers,  and  the  training  of  them  so  as  to  attain  their 
highest  activit}'^  and  fullest  development.  As  in  the  culture 
of  land  we  him  to  improve  the  soil,  so  in  human  cultui-e  we 
aim  to  enrich  the  soil  of  the  mind  and  cause  it  to  bud  and 
blossom  and  bring  forth  its  richest  harvests  of  thought  and 
sentiment,  of  science,  art,  and  character. 

Culture  is  usually  divided  into  three  distinct  branches; 
Physical  Culture,  Intellectual  Culture,  and  Moral  and  Relig- 
ious* Culture.  Besides  these  there  are  also  Social  Culture, 
^Esthetic  Culture,  Spiritual  Culture,  etc.  These  are,  however, 
but  varieties  or  special  forms  of  those  before  mentioned,  which 
are  the  ones  generally  embi-aced  in  a  scheme  of  education. 

Physical  Culture. — Physical  Culture  is  that  which 
relates  to  the  cultivation  and  development  of  the  physical 
powers.  It  embraces  the  culture  and  attainment  of  Health, 
Strength,  Skill,  and  Beauty.  A  full  discussion  of  the  subject 
would  include  a  consideration  of  the  conditions,  the  laws,  and 
the  methods  of  securing  each  one  of  these  objects. 

The  first  object  of  physical  culture  is  Health.  To  a  large 
extent  man's  health  is  in  his  own  keeping.  We  can  be  sick 
or  well  as  we  choose.  Sickness  is  the  penalty  of  violating 
physical  law.  Death,  except  in  old  age,  is  a  curse  entailed 
upon  man  by  his  transgressions.  A  proper  physical  culture 
would  banish  disease  and  premature  death  from  the  land.  It 
would  increase  the  average  term  of  life  from  thirty-three  to, 
at  least,  threescore  and  ten  j-ears.     Physical  culture  seeks  to 

(37) 


38  METHODS   OF   TEACHING. 

ascertain  the  laws  and  methods  by  which  these  results  are 
secured,  and  to  present  a  sound  body  as  a  condition  of  a 
sound  and  vigorous  intellect. 

The  second  object  of  physical  culture  is  Slretiyth.  By  cul- 
ture a  man  can  double  or  treble  his  natural  strength  ;  and  not 
transcend  the  limits  of  health.  A  proper  physical  culture 
would  remove  the  bodily  weakness  which  we  find  so  prevalent 
in  society.  It  would  give  muscular  fibre  and  endurance  where 
we  now  find  flabbiness  and  debility.  It  would  give  physical 
power  to  our  professional  and  business  men,  and  enable  them 
to  endure  much  more  fatigue  and  to  accomplish  nnuch  more 
than  they  can  at  present.  It  would  transform  the  delicate 
and  frail-looking  women  of  to-day,  who  cannot  go  upstairs 
without  palpitation  of  the  heart,  or  see  a  spider  without  faint- 
ing or  shrieking,  into  women  of  muscular  power  and  endur 
ance,  such  as  were  the  women  of  Sparta,  and  as  nature 
intended  women  to  be. 

The  third  object  of  physical  culture  is  Skill.  This  is  also 
an  object  worthy  of  attainment.  To  use  the  muscles  with 
dexterity,  either  for  pleasure  or  business,  is  in  itself  laudable. 
There  is  a  merit  in  being  a  good  g3'mnast,  or  a  good  cricketer 
or  base  ball  player.  To  walk  far,  run  fast,  jump  a  good  dis- 
tance, etc.,  are  not  unworthy  attainments.  It  is  told  to  the 
credit  of  Washington  that  he  could  leap  twentj'-four  feet  on 
a  running  jump.  To  possess  manual  skill  and  be  able  to  use 
our  hands  for  some  useful  purpose  is  especiallj^  desirable. 
A  knowledge  of  a  use  of  tools  is  of  great  value  to  every 
person.  "  Every  man  his  own  carpenter"  is  worth  as  much 
as  "  every  man  his  own  lawyer."  Education  should  therefore 
aim  to  cultivate  muscular  skill  and  dexterity'. 

A  fourth  object  of  physical  culture  is  the  attainment  of 
Beauty.  Deformity,  like  siclaiess,  is  the  result  of  vioUited 
phj'sical  law.  Had  sin  never  entered  Paradise,  men  woukl 
be  as  handsome  as  Adam,  who  was  no  doubt  a  model  in 
phj-sical  proportion  ;  and  womer.  would  still  be  as  lovely  as 


NATURE    OF   CULTURE.  39 

Eve,  who  was,  it  is  believed,  the  perfection  of  womanly  beauty. 
Let  the  race  keep  nature's  laws,  and  we  would  return  towartl 
the  primitive  beauty  fashioned  by  the  Divine  hand.  Art  does 
much  to  restore  what  we  have  lost ;  but  culture  is  the  best 
panacea  for  ugliness.  The  best  coloring  for  the  cheek  is 
pure,  rich  blood;  the  best  enamel  for  the  neck  and  arms  is 
the  flush  of  health.  Such  beauty  does  not  rub  off  nor  come 
and  go  with  the  touch  of  art — "  'T  is  ingrain  ;  't  will  endure 
Vvind  and  weather." 

Intellectual  Culture Intellectual    Culture    is    that 

which  relates  to  the  development  and  training  of  the  intellect- 
ual powers.  The  object  of  intellectual  culture  is  the  normai 
growth  and  highest  activity  of  all  the  intellectual  faculties. 
A  full  consideration  of  the  subject  would  present  the  laws 
and  methods  b}-  which  each  susceptibility^  and  power  may  be 
properl3'  trained  and  developed.  Only  a  few  thoughts  will 
be  here  presented. 

Intellectual  Culture  aims  to  cultivate  the  powers  of  Obser- 
vation. It  enables  man  to  see  what  is  going  on  around  him, 
and  to  acquire  a  knowledge  of  facts  and  phenomena.  It 
makes  him  sharp-eyed  and  ready  to  drink  in  knowledge  at 
every  pore.  It  makes  him  an  original  observer  of  nature  and 
society,  obtaining  his  knowledge  first  hand,  instead  of  de- 
pending on  others  for  it.  It  thus  gives  him  independence  in 
his  own  ideas  of  things,  and  enables  him  to  make  contribu- 
tions to  the  sum  of  human  knowledge. 

Intellectual  Culture  increases  the  power  of  the  Memory 
It  gives  strength  of  retention  and  readiness  of  recollection 
It  makes  man  a  treasury-  of  knowledge, — a  walking  library  of 
information.  It  aims  to  overcome  the  habit  of  allowing 
things  to  fade  away  from  the  memory,  and  trains  the  mind 
to  hold  what  is  worth  knowing  as  a  permanent  possession.  It 
aims  to  bring  the  memory  up  towards  the  old  standard  of 
power  when  men  could  repeat  volumes  of  manuscript,  or  "call 
by  name  the  twentv  thousand  citizens  of  Athens." 


40  METHODS    OF   TEACHING. 

Intellectual  Culture  aims  to  give  activity  and  direction  to 
the  power  of  Imagination.  It  leads  it  to  delight  in  ideal 
creations,  to  enjoy  the  works  of  fiction,  to  wander  with  pleas- 
ure among  the  images  of  poetr}^,  to  linger  delighted  amid  the 
romantic  events  of  history,  to  awaken  into  activity  in  view- 
ing the  varied  beauties  of  earth,  sea,  and  sky,  and  to  revel 
among  the  works  of  art  where  the  pencil  of  the  painter  or 
chisel  of  the  sculptor  has  made  a  name  immortal.  It  aims 
also  to  develop  the  creative  power  of  artistic  genius,  and  to 
stimulate  those  who  have  the  gift  divine  to  emulate  the  achieve- 
ments of  the  masters  in  poetry,  fiction^and  fine  art. 

Intellectual  Culture  embraces  the  training  of  the  power  of 
Thought.  It  aims  to  make  man  a  thinker,  to  enable  him  to 
draw  true  conclusions  from  the  facts  he  observes,  to  exercise 
correct  judgment  in  the  affairs  of  life,  to  investigate  and  ascer- 
tain the  laws  of  nature  and  society,  to  read  the  truths  which 
God  has  written  upon  the  pages  of  earth  and  sky,  to  build  up 
the  sciences  and  apply  their  principles  to  the  advancement  of 
truth  and  the  improvement  of  the  world.  It  aims  to  develop 
the  power  of  thought  by  which  man  lifts  himself  into  a  higher 
civilization,  makes  the  elements  servants  of  his  will  to  pro- 
mote his  comfort  and  happiness,  arms  himself  with  the  power 
to  predict  the  events  of  the  far  off"  future,  and  stands  at  the 
head  of  created  beings,  crowned  with  the  triumphs  of  science 
and  philosophy. 

JEsthetic  Culture. — J^sthetic  Culture  embraces  the  culti- 
vation of  the  aesthetic  nature.  The  aesthetic  nature  includes  the 
activity  of  the  Reason  and  the  Sensibilities  as  pertaining  to 
the  beautiful.  The  Reason  apprehends  beauty  ;  the  Sensibili- 
ties admire,  appreciate,  and  enjoy  it.  Esthetic  culture  seeks 
to  develop  this  nature  to  the  fullest  appreciation  of  the  element 
of  beauty  as  found  in  the  works  of  nature  and  art,  to  lift  the 
soul  upward  to  the  enjoyment  of  the  refined  and  artistic,  to 
refine  and  elevate  the  taste,  and  thus  add  to  man's  happiness 
and  lend  an  influence  for  the  growth  of  his  spiritual  nature. 


NATURE    OF    CULTURE.  41 

Moral  Culture. — Moral  Culture  embraces  the  training  of 
the  moral  nature.  The  moral  nature  includes  the  activity  of 
the  entire  spiritual  being;  it  involves  the  activity  of  the 
Intellect,  the  S'^nsibilities  and  the  Will.  The  Reason  appre- 
hends the  Right  and  the  obligation  to  do  the  Right;  the  Sensi- 
bilities feel  the  obligation  to  act  in  accordance  with  an  appre- 
hension of  obligation  ;  and  the  Will  puts  forth  the  executive 
volition  in  obedience  to  the  spiritual  imperative.  The  M%- 
thetic  nature  consists  of  idea  and  feeling;  the  Moral  nature 
consists  of  idea,  feeling,  and  will.  In  mathematical  phrase- 
ology, the  ^Esthetic  nature=the  Reason,  plus  the  Sensibilities ; 
the  Ethical  nature=the  Reason,  plus  the  Sensibilities,  plus 
the  Will.  Moral  Culture  embraces  the  full  and  complete  de- 
velopment of  this  nature. 

Jieligious  Cultm^e. — Religious  Culture  embraces  the  train- 
mg  and  development  of  the  religious  nature.  The  religious 
nature  is  the  highest  form  of  the  ethical ;  it  is  the  ethical 
acting  in  relation  to  the  Supreme  Being.  It  implies  the  con- 
secration of  all  our  powers  to  God,  and  requires  their  fullest 
and  highest  activity.  The  highest  operation  of  the  Reason 
is  Faith  ;  the  highest  operation  of  the  Sensibilities  is  Love  ; 
the  highest  operation  of  the  Will  is  Obedience.  The  elements 
of  religion,  therefore,  are  Faith,  Love,  and  Obedience  ;  Faith 
in  God  and  salvation  ;  Love  to  God  and  man  ;  Obedience, 
the  complete  subordination  of  the  human  will  to  the  Divine. 
Here  w^e  reach  the  crowning  excellence  of  man's  being,  the 
keystone  of  the  spiritual  arch.  Religious  culture  thus  aims 
to  cultivate  faith  in  God,  love  to  God  and  man,  and  complete 
obedience  to  the  Divine  will. 


CHAPTER  YI. 

METHODS    OF   CULTIVATING   EACH    FACULTY. 

HAVING  attained  a  knowledge  of  the  nature  of  the  mind 
and  the  general  nature  of  culture,  we  are  prepared  to 
apply  these  to  the  training  of  each  faculty'  of  the  mind.  Only 
a  few  brief  suggestions  can  be  made ;  the  subject  would 
require  a  volume  to  treat  it  with  any  degree  of  completeness. 

Perception. — The  Perceptive  Powers  should  be  cultivated 
in  early  childhood.  This  is  indicated  by  Nature,  who  gives 
active  senses  to  a  little  child.  Teachers  haA'e  been  entirely 
too  neglectful  of  their  duty  in  this  respect.  Children  have 
not  been  trained  to  use  their  eyes  and  their  other  senses  as 
they  should  have  been.  They  have  been  taught  to  read  the 
text-books  of  the  school-room  ;  but,  to  a  large  extent,  the 
"book  of  Nature"  has  been  a  sealed  volume  to  them. 

The  Perceptive  Powers  may  be  cultivated  by  training  chil- 
dren to  a  habit  of  observation.  The  following  suggestions 
will  indicate  to  teachers  the  method  of  cultivating  the  per- 
ceptive faculty : 

1.  To  cultivate  the  Perceptive  Powers,  require  pupils  to 
observe  things  for  themselves.  Bring  objects  into  the  school- 
room for  them  to  see  and  examine.  Send  them  out  into  the 
fields  and  woods  to  gather  facts  for  themselves.  Teach  them 
to  read  the  book  of  nature  as  well  as  the  books  of  the  school- 
room. 

2.  To  cultivate  the  Perceptive  Powers,  require  pupils  to 
describe  objects.  In  order  to  descrilje  an  object,  it  must  be 
very  closely  observed.  The  attempt  to  describe  will  lead 
pupils  to  see  the  necessity  of  examining  an  olvject  with  atten- 
tion, and  will  give  quickness  and  accuracy  to  the  perceptive 
powers.  ^  ^2  ^ 


CULTIVATING   EACH   FACULTY.  4b 

3.  To  cultivate  the  Perceptive  Powers,  train  pupils  upon  a 
well  graded  system  of  object-lessons.  Give  the  pupils  lessons 
on  form,  color,  size,  etc.,  and  they  will  learn  to  notice  these 
elements  in  the  objects  that  they  see.  The  sense  of  vision 
will  thus  become  sharp,  delicate,  and  accurate. 

4.  Require  pupils  to  draw  outlines  or  sketches  of  objects. 
In  order  to  draw  an  outline  of  an  object  it  is  necessary  to 
examine  it  very  minutely.  The  practice  of  drawing  Avill 
thus  cultivate  the  habit  of  close  and  minute  observation. 

Such  exercises  will  train  pupils  to  the  habit  of  using  their 
perceptive  powers,  and  habit  is  nearly  everything  in  educa- 
tion. Teachers  should  also  impress  upon  the  minds  of  their 
pupils  the  importance  of  using  their  eyes,  and  not  going 
through  the  world  blind  to  its  most  interesting  facts. 

The  3Iemory. — The  Memory  should  be  carefully  trained 
in  youth,  so  that  it  may  firmly  hold  the  knowledge  acquired 
and  readily  recall  it.  Minds  differ  in  natural  power  of  mem- 
ory, but  much  can  be  done  to  strengthen  a  weak  or  quicken  a 
sluggish  memory.  A  neglect  of  the  proper  use  of  this  faculty 
leads  to  habits  which  weaken  it,  and  make  it  slow  to  acquire 
and  unreliable  in  recalling  its  knowledge. 

The  followinsr  suo;o;estions  will  indicate  to  the  teacher  how 
he  may  cultivate  the  memory  of  his  pupils : 

1.  To  cultivate  the  Memory ,  require  pujnls  to  attend  closely 
to  xohatever  subject  they  are  considering.  Attention  is  a 
necessary  condition  of  remembering.  A  heedless  mind  soon 
forgets  what  it  sees,  hears,  or  reads.  The  mind  must  be  con- 
centrated upon  the  object  of  thought  that  it  maj-  be  indelibly 
impressed  ui)on  the  memory. 

2.  To  cultivate  the  Ifemory,  lead  jmpils  to  feel  an  interest 
in  ivhat  you  wish  them  to  remember.-  An  interested  mind  is 
open  to  receive  the  deepest  impression.  An  incident  which 
excites  the  mind  is  never  forgotten.  A  pupil  who  takes 
delio;ht  in  what  he  is  learning  will  have  little  difficultv  in 
acquiring  it,  and  will  retain  it  permanently. 


44  METHODS   OF   TEACHING. 

3.  To  cultivate  the  Memory^  we  should  require  a  frequent 
review  or  repetition  of  that  which  the  pupil  has  learned. 
Repetition  seems  to  fix  a  subject  more  firmly  in  the  memory. 
It  acts  like  the  die  on  a  waxen  tablet ;  every  repetition  seems 
to  make  the  impression  more  durable.  The  subject  most  fre- 
quently recited  is  the  most  readily  recalled,  and  remains  the 
longest  in  the  memory. 

4.  To  cultivate  the  Memory^  we  should  require  pupils  to 
commit  many  extracts  of  prose  and  poetry.  This  will  fix 
words  and  forms  of  expression  in  the  mind,  and  cultivate  a 
memory  for  language.  Practice  of  this  kind  will  give  great 
facility  in  committing,  while  a  neglect  of  it  will  so  enfeeble 
the  memory  that  it  will  be  almost  impossible  to  commit  any- 
thing. 

5.  -To  cultivate  the  Memory,  we  should  lead  the  pupils  to 
connect  their  knowledge  by  the  laws  of  association.  This  is 
the  way  in  which  the  memory  naturally  acts,  and  in  which  it 
acts  with  the  most  readiness  and  accuracy.  The  pupil  should 
associate  similar  facts  in  geography,  events  of  the  same  date 
in  history,  or  those  related  as  cause  and  effect.  Such  a  habit 
will  give  a  strong  and  reliable  memory. 

Tiie  Imagination. — The  Imagination  of  children  should 
be  carefully  cultivated.  This  faculty  is  usually  very  active 
in  childhood,  and  needs  guiding  and  refining.  When  it  is 
sluggish,  it  should  be  excited  and  aroused  into  activity;  when 
it  is  too  active,  it  should  be  restrained  and  directed.  The 
judicious  training  of  this  faculty  will  be  of  great  value  to 
the  pupil.  It  will  be  a  source  of  pure  and  refined  pleasure, 
and  will  exert  an  elevating  influence  on  the  character. 

1.  The  Imagination  may  be  cultivated  by  observing  beauti- 
fd,  grand,  and  picturesque  scenery.  The  spreading  land- 
scape, the  flowing  river,  the  wide  extended  ocean,  the  arching 
sky,  out  of  whose  deep  blue  the  golden  stars  are  shining,  the 
moon  in  her  beauty  and  the  sun  in  his  splendor — all  these 
tend  to  give  activity  and  culture  to  the  imagination. 


CULTIVATING  EACH   FACULTY.  46 

2.  The  Imagination  may  he  cultivated  by  filling  the  memory 
ivith  beautiful  pictures  of  natural  scenery.  The  beautifuJ 
objects  we  have  seen  should  be  brought  before  the  mind  as 
pictures  upon  which  it  delights  to  look.  Each  mind  may 
thus  be  a  gallery  where  pictures  of  beauty  hang  upon  the 
walls  of  memory,  exciting  the  imagination  to  activity  and 
furnishing  it  with  pure  and  lofty  ideals. 

3.  The  Imagination  may  be  cultivated  by  reading  poetry^ 
fiction^  and  other  imaginative  compositions.  Such  produc- 
tions are  the  embodiments  of  the  imaginings  of  others,  and 
awaken  our  own  imaginations  into  activity.  The  figures  of 
the  poet,  the  characters  and  incidents  of  fiction,  linger  in  the 
memory  and  stimulate  us  to  create  for  ourselves  such  images 
of  beaut}''  and  incidents  of  life. 

4.  The  Imagination  may  be  cultivated  by  hearing  music, 
visiting  galleries  of  painting,  statuary,  etc.  Here  we  have 
the  embodiment  of  imaginative  beauty  in  color  and  form, 
which  pleases  and  excites  the  fancy.  That  which  was  once  in 
the  imagination  of  the  creator  awakens  a  similar  activit}'  in 
the  mind  of  the  beholder.  There  is  thus  cultivated  a  pure 
and  refined  taste,  and  a  natural  and  lively  activit}^  of  the 
Imagination. 

5.  The  Imagination  may  be  cultivated  by  creating  imagin- 
ary scenes,  incidents,  etc.  The  creative  power  of  the  Imag- 
ination is  its  highest  office,  and  such  exercise  gives  it  ihe 
highest  culture.  The  pupils  can  be  led  to  create  and  describe 
ideal  landscapes  or  incidents  of  human  action.  They  may  be 
required  to  write  and  relate  imaginary  or  fictitious  events,  as 
allegories,  parables,  novelettes,  etc.  Poetical  composition 
and  the  creating  of  figures  of  rhetoric  aflford  valuable  culture 
in  this  respect. 

The  Understanding. — The  Understanding  of  children 
should  also  be  carefully  trained.  Pupils  should  be  taught  to 
think,  as  well  as  to  see  and  remember.  Care  should  be  taken 
that  the  memor}"  be  not  required  to  do  that  which  the  under- 


i6  METHODS   OF   TEACHING. 

standing  of  the  child  should  perform.  Perhaps  the  greatest 
mistake  of  school  work  is  made  jnst  at  this  point.  There  ia 
often  too  much  cramminor,  and  not  enouah  thinking  in  our 
schools. 

1.  The  Understanding  may  he  cultivated  by  the  study  of 
thought  studies,  as  ]i[ental  Arithmetic,  Written  Arithmetic, 
Grammar,  Geometry^  etc.  These  studies  require  pupils  to 
think,  and  pupils  learn  to  think  b}'  thinking.  Care  should  be 
taken  that  the  pupils  study  with  the  understanding  and  not 
merely  with  the  memory. 

2.  The  Understanding  may  lie  cultivated  by  working  out 
original  problems,  parsing  and  analyzing  sentences,  etc. 
These  exercises  require  the  pupils  to  employ  the  power  of 
original  thought.  They  lead  the  mind  to  compare,  and  the 
process  of  comparison  lies  at  the  foundation  of  thinking. 
The  judgment  must  be  exercised  to  apply  the  principles  and 
rules,  and  to  see  the  relation  of  the  conditions  of  the  problem 
or  the  elements  of  the  sentence. 

3.  The  Understanding  may  be  cultivated  by  writing  compo- 
sitions and  trying  to  think  out  and  express  something  new. 
Such  exercises  bring  into  activity  the  inventiA-e  powers  of  the 
mind.  They  require  the  pupil  to  elaborate  his  knowledge,  to 
work  it  up  into  new  forms,  to  think  out  something  new  for 
himself.  Writing  original  compositions  is  thus  a  most  excel- 
lent exercise  for  the  cultivation  of  thought-power. 

4.  The  Understanding  may  be  cultivated  by  the  study  of  the 
mathematical  and  physical  sciences.  The  three  best  studies 
to  develop  the  power  of  thought  are  Mental  Arithmetic,  for 
the  young  student ;  Geometry,  for  students  from  fourteen  to 
eighteen  j-ears ;  and  Mental  Philosophy  and  Logic,  from 
eighteen  years  and  upward.  For  inductive  thought,  the  nat- 
ural sciences  should  be  studied ;  as  Botany  and  Natural 
Philosoph3\  The  former  teaches  pupils  to  generalize  and  clas- 
sify ;  the  latter  to  investigate  the  causes  and  laws  of  things. 

5.  The  Understanding  may  he  cultivated   by  reading   the 


CULTIVATING    EACH    FACULTY.  47 

icorks  of  the  great  thinkers.  To  follow  thought,  as  ex})rcssed 
in  language,  will  stimulate  to  thinking.  By  reading  the  works 
of  Plato,  Aristotle,  Bacon,  Hamilton,  etc.,  the  mind  becomes 
familiar  with  great  thoughts  and  is  aroused  to  think  for  itself. 

6.  The  Understanding  mai/  be  cultivated  by  thinking.  We 
learn  to  think  by  thinking,  thinking,  thinking. 

Attention. — The  power  of  Attention  should  be  carefully 
trained  in  childhood.  It  is  one  of  the  most  important  of  the 
mental  powers,  for  upon  its  actiA'it}'  depends  the  eflicieney  of 
each  one  of  the  specific  faculties.  Mental  power  is,  to  a  large 
extent,  the  power  of  attention  ;  and  genius  has  been  defined  as 
"  nothing  but  continued  attention." 

The  following  suggestions  will  indicate  to  the  teacher  the 
methods  by  which  the  power  of  attention  can  be  cultivated : 

1.  Have  pu^Dils  observe  objects  closely. 

2.  Require  them  always  to  study  with  close  attention. 

3.  Read  long  sentences  and  have  pupils  write  them. 

4.  Read  quite  long  combinations  in  mental  arithmetic,  and 
have  pupils  repeat  them. 

5.  Mathematical  studies  are  especially  valuable  in  cultivat- 
ing the  power  of  attention. 

The  following  suggestions  are  made  to  aid  a  teacher  in 
securing  the  attention  of  his  pupils : 

1.  Manifest  an  interest  in  the  subject  you  are  teaching. 

2.  Be  clear  in  your  thought,  and  ready  in  your  expression. 

3.  Speak  in  a  natural  tone,  with  variet}^  and  flexibility  of 
voice. 

4.  Let  the  position  before  the  class  be  usually  a  standing 
one. 

5.  Teach  without  a  book,  as  far  as  possible. 

().  Assign  subjects  promiscuously,  when  necessary. 

7.  Use  the  concrete  method  of  instruction,  when  possible. 

8.  Yary  your  methods,  as  A-ariety  is  attractive  to  children, 

9.  Determine  to  secure  the  attention  at  all  hazards. 


CHAPTER  VII. 

THE   NATURE   OF    KNOWLEDGE. 

IN  order  to  give  instruction  skillfully,  a  teacher  should  have 
an  idea  of  the  general  nature  of  the  different  branches  of 
knowledge  and  their  relations  to  one  another.  He  should  see 
clearly  the  elements  of  which  the  different  branches  are  com- 
posed, the  relation  of  these  elements  to  the  human  mind, 
and  the  manner  in  which  the  sciences  are  developed.  We 
shall,  therefore,  present  a  brief  discussion  of  the  Nature  of 
Knowledije. 

Common  and  Scientific. — All  knowledge  may  be  embraced 
under  two  general  divisions  ,  Common  Knowledge  and  Scien- 
tific Knowledge.  Common  Knowledge  consists  of  unsystem- 
atized facts,  ideas,  and  truths.  It  is  a  knowledge  possessed  by 
the  common  people,  and  is  the  basis  of  Scientific  Knowledge. 
Scientific  Knowledge  consists  of  facts,  ideas,  and  truths,  sys- 
tematized and  expressed  in  the  form  of  laws  and  principles. 
It  enables  man  to  interpret  the  facts  and  phenomena  of  nature, 
to  see  the  great  laws  by  which  the  universe  is  governed,  and 
to  previse  and  predict  the  events  of  the  future. 

General  Division  of  Science. — Scientific  knowledge  has 
been  divided  into  two  general  branches;  the  Empirical 
Sciences  and  the  Rational  Sciences.  This  classification  is 
based  upon  the  relation  of  their  subject  matter  and  methods 
of  development  to  the  human  mind. 

The  Empirical  Sciences  are  those  which  are  founded  on  the 
knowledge  derived  through  the  senses:  they  are  developed 
oy  Generalization,  Classification,  and  Inductive  Reasoning. 
Geography,  Botany,  and  Natural  Philosophy  are  examples  of 
the  empirical  sciences.     The  facts  of  these  sciences  are  givea 

(48) 


THE    NATURE    OF    KNOWLEDGE.  49 

by  Perception:  these  facts  are  classified  by  Generalization, 
and  their  laws  and  causes  are  derived  !);>•  Induction. 

The  Rational  Sciences  are  those  which  are  founded  on  tlie 
knowledge  given  by  Intuition  or  the  Reason:  they  are  devel- 
oped b}'  Deductive  Reasoning.  Arithmetic,  Geometry,  Logic, 
etc.,  are  examples  of  the  rational  sciences.  The  fundamental 
ideas  and  axiomatic  truths  of  these  sciences  are  given  by 
Intuition,  and  their  dei'ived  truths  are  obtained  by  Deduction. 

Schemes  of  Clas.sificafion. — There  have  been  many  at- 
tempts made  to  classify  knowledge ;  but  no  scheme  of  classi- 
fication has  yet  been  presented  which  has  been  universally 
accepted.  Comte,  the  celel)rated  positive  philosopher,  classi- 
fies the  sciences  with  respect  to  the  matter  of  which  they  are 
composed.  His  classification  i^  as  follows :  Mathematics, 
Astronomy,  Physics,  Chemistry,  Physiolog3%  and  Social 
Phvsics.  Dr.  Hill  classifies  the  branches  according  to  the 
order  of  their  development.  His  classification  is  Mathesis, 
Physics,  History,  Psychology,  and  Theology.  Dr.  Wicker- 
sham  groups  the  sciences  together  under  the  following  heads: 
The  Elements  of  Knowledge,  Language,  The  Formal  Sciences, 
The  Empirical  Sciences,  The  Rational  Sciences,  The  Histori- 
cal Sciences,  and  The  Arts. 

Author's  Classification Without  discussing  these  sev 

era!  schemes  o.f  classification,  we  sl?all  present  one  which  we 
think  best  suited  to  the  training  of  young  teachers.  Knowl- 
edge may  be  classified  into  seven  principal  divisions:  1.  Lan- 
guage, 2.  Mathematics,  3.  Physics,  4.  History,  5.  The  Arts, 
6.  Psychology,  T.  Theology.  This  classification  is  simple, 
and  has  the  advantage  of  employing  the  names  of  the  branches 
as  generally  used  in  our  schools. 

These  general  branches  and  their  subdivisions  are  not 
always  entirely  distinct  from  one  another.  They  often  over- 
lap one  another  and  intrnde  upon  one  another's  territory.  It 
is  impossible  to  draw  a  line,  in  every  case,  marking  just  where 
one   branch   ends   and   another   begins.     This    ig    tru«  witli 


50  METHODS   OF   TEACHINa. 

respect  to  every  classification  that  has  been  attempted.  The 
scheme  here  presented  seems  more  satisfactory,  for  the  pur- 
pose of  teaching,  than  any  that  we  have  met. 

Laiiffuage. — Language  is  the  instrument  of  thought  and 
the  medium  of  expression.  The  term  is  derived  from  lingua, 
the  tongue.  Primarily,  Language  is  the  means  of  communi- 
cating knowledge  :  it  enables  one  mind  to  ti'ansfer  its  thought 
to  another  mind.  It  is  also  found  that  language  is  the  means 
by  which  we  think,  as  well  as  the  medium  by  which  we  com- 
municate our  thoughts.  We  cannot  think  to  any  great 
extent,  if  at  all,  without  language;  and  the  more  perfect  our 
language  the  more  powerful  mir  thought — as  in  algebra,  arith- 
metic, etc  We  therefore  embrace  these  two  uses  of  language 
in  our  definition,  and  define  it  to  be  the  instrument  of  thought 
and  the  medium  0/  expression. 

JIatheniatics — Mathematics  is  the  science  of  Quantity. 
The  term  is  derived  from  mathematike,  meaning  science.  It 
investigates  the  relations  of  quantity,  and  unfolds  the  trutlig 
and  jjrinciples  belonging  10  it.  It  is  based  on  intuitive  ideas 
and  truths,  and  developed  by  deductive  reasoning.  The  three 
principal  branches  are  Arithmetic,  Geometry,  and  Algebra. 
Arithmetic  is  the  science  of  Number;  Geometry  is  the  science 
of  Space ;  Algebra  is  a  general  method  of  investigating  all 
kinds  of  quantity  by  means  of  sj^mbols. 

J*/il/.sics. — Physics  is  the  science  of  the  material  world. 
The  term  is  derived  from  phusis,  nature.  It  consists  of  facts 
and  phenomena,  and  the  laws  and  principles  which  control 
them.  It  begins  with  the  observation  of  facts,  compares  and 
classifies  them,  and  ascertains  the  causes  which  give  rise  to 
them  and  the  laws  which  control  them.  The  principal 
branches  are  Geography,  Natural  History,  Natural  Philoso- 
phy, Astronomy,  Chemistry,  Geology,  etc. 

Geography  treats  of  the  facts  relating  to  the  surface  of  the 
earth,  classifies  them,  and  investigates  their  causes,  and  the 
laws  which  govern  them.     Natural  history  treats  of  the  three 


THE   NATURE    OF    KNOWLEDGE.  51 

kingdoms  of  nature, — the  mineral,  the  vegetable,  and  the  ani- 
mal, — ascertaining  the  nature,  structure,  etc.,  of  the  indi- 
vidual objects,  and  classif}- ing  them.  It  includes  Mineralogy, 
Botany,  and  Zoology.  Natural  Philosophy  treats  of  the  facts 
and  phenomena  of  nature,  and  ascertains  their  causes  and  the 
laws  which  govern  them.  It  includes  Mechanics,  Optics, 
Acoustics,  etc.  Astronomy  treats  of  the  facts  and  truths 
relating  to  the  heavenly  bodies.  Chemistry  treats  of  the  na- 
ture and  properties  of  the  elements  of  bodies.  Geology  treats 
of  the  origin,  development,  and  structure  of  the  earth. 

History. — History  is  a  systematic  description  of  the  past 
acts  and  condition  of  mankind.  It  embraces  the  Facts  of 
History  and  the  Philosophy  of  History.  The  Facts  of  History 
embrace  the  events  that  have  occurred  in  the  life  of  individu- 
als and  nations.  The  Philosophy  of  History  endeavors  to 
ascertain  the  causes  which  have  contributed  to  produce  the 
different  changes  in  society  and  nations,  and  thus  to  predict 
the  future  condition  of  the  face.  In  other  words,  it  endeavors 
"  to  solve  the  problem  of  man's  condition  and  destiny." 

Art. — Art  is  the  application  of  knowledge  or  power  to  effect 
some  desired  object.  It  is  the  outgrowth  of  practice,  and  may 
be  defined  as  practice  guided  by  principle.  The  Arts  are 
divided  into  two  general  classes  ;  the  Fine  Arts  and  the  Use- 
ful Arts,  The  object  of  the  Useful  Arts  is  the  attainment  oi 
the  end  of  utility;  the  object  of  the  Fine  Arts  is  the  attain- 
ment of  the  end  of  beauty.  These  two,  though  primarily  dis- 
tinguished, are  often  combined  in  the  same  production  ;  as  in 
the  manufacture  of  glass  and  pottery  ware,  in  architecture, 
engraving,  etc. 

Psychology. — PSYCHOLOGY  is  the  science  of  the  human 
mind.  The  term  is  derived  from  psyche^  the  soul.  It  is 
sometimes  divided  into  Empirical  Psychology  and  Rational 
Psychology.  Empirical  Psychology  treats  of  the  nature  of 
the  mind  as  revealed  in  the  experience  of  consciousness. 
Rational  Psjx'hology  treats  of  the  nature  of  the  mind  as  de- 
termined b}'  the  necessary  principles  given  by  the  Reason. 


52  METHODS   OF   TEACHING. 

TheolofTU — Theology  is  the  science  which  treats  of  God. 
The  term  is  from  Theos,  God,  and  logos,  a  discourse.  It  has 
been  divided  into  Natural  Theolog}^  and  Revealed  Theology. 
Natural  Theology  endeavors  to  ascertain  the  nature  of  God 
through  his  works,  by  the  light  of  philosophy  and  reason. 
Revealed  Theology  seeks  a  knowledge  of  the  Divine  Being 
through  his  revealed  word. 

Ofherr  Distinctions. — It  is  often  convenient  to  speak  of 
the  Inductive  and  the  Deductive  Sciences.  The  former  in- 
clude all  those  branches  of  knowledge  wliich  begin  in  facts 
aiid  are  developed  b}^  generalization  and  inductive  reasoning ; 
as  geography,  botan^',  natural  philosoph}',  etc.  The  latter 
include  all  those  branches  of  knowledge  which  begin  in  ideas, 
and  are  developed  by  the  process  of  deductive  reasoning  ;  as 
arithmetic,  geometry,  etc.  A  division  of  the  Rational  Scien- 
ces is  often  made,  called  the  Formal  Sciences.  The  Formal 
Sciences  may  be  defined  to  be  those  sciences  which  treat  of  the 
necessary  forms  in  which  truth  presents  itself.  They  include 
Mathematics  and  Logic ;  Mathematics  treating  of  the  form  in 
which  quantity  is  presented,  and  Logic  of  the  form  in  which 
thought  presents  itself. 

NoTK. — In  respect  to  Geography,  it  should  be  stated  that  it  is  not  a  dis- 
tinct science,  but  a  combination  of  several  sciences.  Thus  in  its  higher 
departments,  it  embraces  the  elements  of  Astronomy,  Natural  Philosophy, 
and  Geology;  while  that  which  relates  to  man  and  his  works  is  historical 
in  its  nature.  Some  writers  in  view  of  the  latter  fact  class  it  among  the 
historical  sciences.  Political  Geography  seems  to  belong  to  Historj',  and 
Physical  Geography  to  the  Physical  Sciences  ;  and  it  maybe  classed  there- 
fore in  either  of  these  two  divisions  of  knowledge. 


CHAPTER  VIII. 

THE   FORMS  OF  HSrSTRUCTION". 

INSTRUCTION,  as  previously  defined,  is  the  art  of  fur- 
nisliing  the  mind  with  knowledge.  It  is  the  art  of  develop- 
ing knowledge  in  the  mind  of  another.  By  it  we  are  enabled 
to  build  up  in  the  mind  of  the  learner  a  knowledge  of  the 
sciences,  as  an  architect  erects  a  building.  Under  the  direc- 
tion of  a  teacher,  a  science  is  developed  in  the  miad  in  sym- 
metry and  beauty  as  a  temple  is  erected  under  the  guiding 
genius  of  a  skillful  architect. 

Knowledge  may  be  developed  in  the  mind  in  different  ways  ; 
these  different  ways  we  call  Forms  of  Instruction.  There  is  a 
certain  order  in  which  knowledge  should  be  developed  in  the 
mind  ;  this  order  we  call  the  Order  of  Instruction.  There  are 
certain  laws  which  should  guide  a  teacher  in  developing  knowl- 
edge ;  these  laws  we  call  the  Principles  of  Instruction.  In 
discussing  the  Nature  of  Instruction  we  shall  speak  of  the 
Forms  of  Instruction,  the  Order  of  Instruction,  and  the  Prui- 
ciples  of  Instruction. 

The  Forms  of  Instruction  are  the  various  wa^'s  in  which  we 
may  develop  knowledge.  The  principal  Forms  of  Instruction 
are  the  Analytic  and  Synthetic,  the  Concrete  and  Abstract,  the 
Inductive  and  Deductive,  the  Theoretical  and  Practical.  We 
will  define  and  illustrate  each  one  of  these  forms. 

Analytic  and  Synthetic. — Analytic  Instruction  is  that 
form  of  teaching  which  proceeds  from  wholes  to  parts.  Thus, 
if  I  take  a  watch  and  separate  it  into  its  parts,  and  teach  the 
name  and  office  of  each  part  as  I  take  it  to  pieces,  the  process 
is  anal3^tic.  So  in  grammar,  if  I  begin  with  the  sentence  and 
separate  it  into  its  parts,  I  am  using  the  analytic  process.  If 
in  geography  we  begin  with  the  globe  as  a  whole,  and  separate 

(53) 


54  METHODS   OF    TEACHING. 

it  into  land  and  water,  and  come  down  from  continents  and 
oceans  to  the  smaller  divisions,  the  process  is  anal3^tic. 

Synthetic  Instruction  is  that  form  of  instruction  which  pro- 
oeeds  from  parts  to  wholes.  Thus,  if  we  take  the  parts  of  a 
watch  as  separated,  and  putting  them  together,  teach  the  name 
and  use  of  each  part,  we  are  teaching  synthetically.  If  in 
grammar  we  begin  with  the  words  as  parts  of  speech,  and  put 
them  together  to  form  sentences,  we  are  teaching  by  the  s^-n- 
thetic  method.  So  if  we  begin  with  the  geography  of  the 
school  grounds,  go  out  to  that  of  the  township,  the  county, 
and  the  state,  and  thus  at  last  cover  the  entire  surface  of  the 
earth,  the  method  is  sj'nthetic. 

Concrete  and  Abstract-. —  Concrete  Instruction  is  that 
form  of  teaching  which  employs  objects  and  illustrations. 
Thus,  object  lessons,  or  the  use  of  pictures  and  diagrams,  are 
examples  of  concrete  instruction.  In  Arithmetic,  the  teaching 
of  the  fundamental  operations  by  means  of  the  numeral 
frame,  of  fractions  by  means  of  illustrations,  of  denominate 
numbers  by  means  of  the  actual  measures,  of  banking  by 
establishing  a  bank  in  the  school,  are  examples  of  concrete 
instruction.  Grammar  taught  from  language,  rather  than 
from  the  rules  of  the  text-book,  is  also  concrete  teaching. 

Abstract  Instruction  is  that  form  of  teaching  which  does 
not  employ  objects  and  illustrations.  In  Arithmetic,  counting, 
addition,  etc.,  taught  without  any  objects  or  illustrations, 
denominate  numbers  by  merely  repeating  the  tables,  per- 
centage by  the  definitions  and  rules  without  illustrating  the 
actual  business  transactions,  etc.,  are  examples  of  abstract 
instruction.  Grammar  taught  from  the  definitions  of  the 
text-books,  instead  of  from  language  in  which  we  find  the 
principles  embodied,  is  abstract  instruction.  Teaching  Geog- 
raphy from  the  book,  rather  than  from  natural  objects,  is  an 
example  of  abstract  instruction. 

Inductive  and  Deductive. — Inductive  Instruction  is  that 
form  of  teaching  which  proceeds  from  particulars  to  generals. 


THE    FORMS    OF   IXSTRUCTION.  55 

The  leading  oi"  |nipils  b}^  appropriate  questions  and  examples 
to  the  apprehension  of  an  idea  or  [irineiple  before  it  is  stated, 
is  a  process  of  inductive  teaching.  Thus,  in  Arithmetic,  if  by 
presenting  particular  examples  we  lead  tlie  pupil  to  see  the 
principle  or  rule  before  stating  it,  wc  teach  inductively.  If 
in  Geometr}',  In'  approi)riate  examj^les,  we  lead  the  pupil  to 
a  geometrical  idea  or  principle,  and  then  require  him  to 
express  it,  we  are  teaching  inductively.  In  Grammar,  teach- 
ing inductively,  we  would  lead  a  pupil  to  the  idea  of  a  part  of 
speech  before  we  named  and  defined  it;  or  lead  him,  as  we 
often  can,  to  the  name  of  a  part  of  si>eech,  without  his  learning 
it  from  a  book  or  the  teacher. 

Deductive  Instruction  is  that  fomi  of  teaching  which  pro 
ceeds  from  generals  to  particulars.  If  we  first  state  the  gen- 
eral principle  and  then  lead  to  the  i^arti«ular  applications  of 
it,  we  are  teaching  deductively.  Thus,  in  Arithmetic,  we  ma}' 
teach  the  pupil  the  principles  of  fractions,  and  then  have  him 
apply  them;  or  in  Grammar  we  may  teach  the  words  of  a 
definition,  and  then  illustrate  its  meaning:  in  botli  cases  we 
are  teachins:  deductively.  Deriving  ideas  from  definitions, 
methods  from  ])rinciples,  particular  methods  from  general 
laws,  are  all  deductive  methods  of  procedure. 

The  Inductive  and  Deductive  methods  ma}'  be  distinguished 
even  in  stating  definitions.  Definitions  ma}'  be  stat-ed  either 
in  an  inductive  or  a  deductive  form.  If  we  begin  with  the 
term  to  be  defined  and  pass  to  its  explanation,  the  form  is 
deductive ;  but  if  we  beixin  bv  o:ivin2r  the  idea,  and  ^nd  by 
naming  the  term,  the  form  is  inductive.  Thus  "  Addition  is 
the  process  of  finding  the  sum  of  two  or  more  numbers,"  is 
in  the  deductive  form ;  and  "  The  process  of  finding  the  sura 
of  two  or  more  numbers  is  called  Addition,"  is  in  the  induc- 
tive form  of  stating  a  definition. 

Theoretical  and  Practical. —  Theoretical  Instruction  is 
that  form  of  teaching  which  deals  principally  with  the  laws 
and  principles  of  a  suiiject.    Teaching  the  tlieory  of  arithmetic 


66  METHODS    OF   TEACHING* 

without  making  an  application  of  it  to  practical  problems,  is 
an  example  of  theoretical  teaching.  The  so-called  practical 
problems  of  arithmetic,  are  sometimes  purely  theoretical, 
never  occurring  in  actual  life.  Teaching  the  definitions  and 
principles  of  grammar  without  apphing  them — a  fault  not 
uncommon — is  also  an  illustration  of  theoretical  instruction. 
The  teaching  of  geometry  without  any  application  of  its  prin- 
ciples to  practical  problems,  a  very  common  fault,  is  also  an 
example  of  theoretical  instruction. 

Pravticol  Instruction  is  that  form  of  teaching  which  deals 
jwincipally  with  the  application  of  the  laws  and  princii)les  of 
a  suV)jcct.  When  pupils  are  required  to  apply  the  principles 
of  arithmetic  to  actual  problems,  and  the  students  of  grammar 
are  taught  to  use  the  princii)les  of  language  in  their  own 
speech  and  writing,  we  have  an  illustration  of  practical  teach- 
ing. To  open  a  counting-house  in  the  school-room  and  show 
by  actual  transactions  what  the  business  problems  of  arith- 
metic mean,  is  practical  instruction.  The  application  of  the 
principles  of  geometr}'  to  actual  problems  that  may  occur  to 
a  business  man,  and  also  to  surveying  and  engineering,  fur- 
nishes an  example  of  practical  instruction. 

Application. — Several  of  these  forms  may  be  used  m  teach- 
ing the  same  subject ;  and  sometimes  one  form  is  preferable 
and  sometimes  another.  The  concrete  and  inductive  forms 
should  be  used  with  children ;  the  abstract  and  deductive 
forms  are  more  suitable  to  older  pupils.  Analysis  and  syn- 
thesis are  often  emploj^ed  in  teaching  the  same  subject ; 
though,  as  a  rule,  the  analytic  form  should  precede  the  sjm- 
thetic.  All  instruction  should  be  practical,  though  at  certain 
stages  the  abstract  element  may  predominate.  It  is  not  our 
])uii^ose  to  point  out  the  use  of  these  forms  here,  but  merely 
to  make  the  pupil  familiar  with  the  forms  themselves,  Their"^ 
use  and  special  application  will  be  indicated  in  the  chapter  on 
the  Principles  of  Instruction,  and  in  the  methods  of  teaching 
the  particular  branches  of  study. 


CHAPTEE  IX. 

THE    ORDER   OF   INSTRUCTION. 

rEIE  school-time  of  life  has  been  divided  into  four  periods ; 
Infancy,  Childhood,  Youth,  and  Manhood.  Infancy  em- 
braces the  period  from  the  birth  of  the  child  to  the  age  of  five 
years  ;  Childhood,  the  period  from  five  to  ten  years  ;  Youth, 
the  period  from  ten  to  sixteen  years  ;  and  Manhood,  the  period 
from  sixteen  to  twenty-one  years. 

These  are  not  definitely  fixed  periods,  as  some  persons 
mature  very  much  earlier  than  others.  Girls  from  twelve  to 
sixteen  years  of  age  are  usually  much  more  mature  than  boys 
of  the  same  age.  The  distinctions  are  suflSciently  definite, 
however,  for  the  purpose  in  view.  The  inquiry  is,  What  is  an 
appropriate  course  of  study  for  each  one  of  these  periods  ? 
How  much  of  the  several  branches — Language,  Mathematics, 
Physics,  History,  the  Arts,  etc.,  shall  be  taught  in  each  one 
of  these  periods  ? 

Several  writers  treat  of  this  subject  under  the  head  of  a 
Graded  Course  of  Study,  in  which  they  attempt  to  fix  the  kind 
and  amount  of  knowledge  suitable  for  the  various  grades  of  a 
public  school.  Dr.  Hill,  who  has  a  very  complete  discussion 
of  the  subject,  divides  the  school  time  into  five  distinct 
grades;  the  first,  or  Sub-primary  school,  from  five  to  eight ; 
the  second  or  Primary  school,  from  eight  to  eleven ;  the  third, 
or  Grammar  school,  from  eleven  to  fourteen;  the  fourth,  or 
High  school,  from  fourteen  to  seventeen  ;  and  the  fifth,  or 
College  period,  from  seventeen  to  twenty-one.  This  is  practi- 
cal ;  but  as  grades  in  different  places  var^',  it  has  been  thought 
best  to  discuss  the  subject  in  general  under  the  four  heads 
named,  as  is  done  b}-  Dr.  Wickersham  in  his  Methods  of  In,' 
3*  (57) 


58  METHODS    OF    TEACHING. 

strnction.  Any  teacher  who  understands  the  order  presented 
will  have  no  difficulty  in  arranging  the  studies  of  a  graded 
school. 

Infancy- — During  this  period  a  child  learns  to  talk.  It 
may  also  learn  a  few  written  words,  and  the  letters  of  the 
alphabet.  In  Mathematics,  it  may  learn  some  of  the  figures 
of  geometry',  to  count  as  far  as  twenty-five  or  fifty,  and  per- 
haps to  add  and  subtract  a  few  of  the  smaller  numbers  with 
objects.  It  will  acquire  a  large  number  of  facts  in  botany  and 
zoolog}-,  and  also  man}-  of  the  elementary  facts  and  phenomena 
of  natural  philosophy-.  It  may  also  become  familiar  with  a 
few  facts  of  history,  learn  to  sing  little  songs,  and  to  use  a 
pencil  and  draw  a  little.  This  instruction  should  be  given  at 
home  or  in  a  kindergarten. 

Childhood. — During  childhood,  the  child  should  learn  to 
read,  to  spell,  to  pronounce  correctly,  and  to  express  itself 
w^ith  considerable  correctness  and  facility,  both  in  speaking 
and  in  writing.  It  should  receive  a  systematic  course  of  in- 
struction in  Language  Lessons,  including  orthography,  the 
construction  of  sentences,  the  use  of  capitals,  punctuation 
marks,  etc.  There  should  not,  however,  be  any  formal  in- 
sti'uction  in  Grammar.  If  circumstances  will  permit,  the  child 
may  learn  to  speak  one  or  two  modern  languages,  and  even 
elementary  instrivction  in  Latin  could  be  given. 

Instruction  in  Arithmetic  should  embrace  numeration  and 
notation, — the  n?ming,  writing,  and  reading  of  numbers ; 
the  fundamental  operations  of  addition,  subtraction,  multipli- 
cation, and  division ;  the  elements  of  common  fractions, 
decimals,  and  denominate  numbers.  In  Geometry,  he  should 
become  familiar  with  all  the  ordinary  figures,  both  plane  and 
solid ;  learn  to  construct  and  point  out  their  different  parts 
and  elements ;  and  perhaps  learn  a  few  of  the  elementary 
truths  of  the  science. 

In  the  facts  of  the  Physical  Sciences,  his  course  should  be 
quite  extensive.     He  should  become  familiar  with  the  leading 


THE    ORDER    OF    INSTR'UCTION.  59 

facts  of  descriptive  geography,  and  be  able  to  locate  the  prin- 
cipal countries,  cities,  rivers,  mountains,  etc.,  of  the  world. 
In  Botan}',  he  should  become  familiar  with  the  ordinary  trees 
of  his  neighborhood,  the  principal  flowers  of  the  garden  and 
meadows,  be  able  to  name  many  of  the  forms  of  leaves 
and  corollas,  etc.  He  should  also  learn  the  names  of  the 
principal  animals,  domestic  and  wild  ;  many  of  the  ordinary 
insects,  and  some  of  the  more  common  fishes.  He  should  also 
learn  the  common  minerals  of  the  neighborhood ;  as  quartz, 
limestone,  sandstone,  granite,  etc.  Manj^  of  the  simple  facts 
and  phenomena  of  Natural  Philosoph3',  and  the  causes  of  the 
same,  vnay  also  be  learned,  and  some  of  the  simpler  experi- 
ments of  the  science  may  be  presented  to  him. 

During  this  period  a  child  can  learn,  by  oral  instruction, 
man}-  of  the  leading  facts  of  the  History  of  the  world,  and  of 
his  own  country.  He  is  able  also  to  read  works  on  biography 
and  histor}',  if  written  in  a  simple  and  interesting  st3'le,  and 
should  be  encouraged  to  do  so.  In  the  Arts,  he  should  be 
taught  to  write,  to  draw,  and  to  sing ;  and  if  he  has  any 
musical  taste,  ma}-  ])egin  to  learn  to  play  some  instrument. 
Boys  should  learn  the  use  of  a  knife  and  other  tools,  and 
girls  the  use  of  tlie  needle,  scissors,  etc. 

Youth. — During  the  period  of  youth,  the  pupil  should  con- 
tinue the  study  of  Language,  increasing  his  vocabulary  and 
acquiring  skill  in  the  use  of  his  mother  tongue.  He  should 
have  a  careful  drill  in  orthography,  pronunciation,  and  read- 
ing. He  should  also  begin  the  study  of  grammar  and  the 
elements  of  rhetoric,  learn  to  use  the  dictionarj-,  and  have 
constant  exercises  in  composition  writing.  He  should  be 
required  to  read,  commit,  and  recite  choice  extracts  of  prose 
and  poetr}-  for  the  cultivation  of  a  literary-  taste.  He  should 
also  begin  the  stud}-  of  Latin  and  Greek,  and  perhaps  one  or 
two  foreign  languages.  An  extensive  course  of  reading  in 
poetry  and  prose  would  also  be  of  advantage. 

In  Mathematics,  he  should  go  through  an  ordinary-  text- 


60  MBH'HDBS   &F   TK ACHING. 

book  on  mental  and  written  arithmetic ;  begin  and  in  many 
eases  complete  an  elemcHtary  work  on  algebra;  and  if  he  has 
had  a  good  opportunity  for  mathematical  study,  should  com- 
plete an  elemeatary  text-book  on  geometry.  Of  the  Physi- 
cal Sciences,  he  should  conitinue  his  course  in  descriptive 
geography,  and  also  study  physiology,  botany,  natural  philoso- 
phy, astronom3',and  physical  geography.  During  this  period 
he  can  complete  the  elements  of  these  branches  as  they  are 
presented  in  the  ordinar}'  elementary'  text-books.  Some  of 
feiie  elements  of  zoology  and  mineralogy  should  also  be  in- 
cluded in  the  course  of  studies  arranged  for  pupils  from  te«  to 
sixteen  years  of  age. 

During  this  period  he  may  complete  the  ordinary  text-book 
on  the  history  of  his  ovax  country,  and  even  a  small  text-book 
on  general  history.  He  should  also  read  such  works  as  the 
Rollo  Books,  Abbott's  Histories,  ajid  other  works  of  bitogra- 
raphy,  travels,  voyages,  and  explorations.  The  historical 
stories  of  Miss  Yonge  and  Miss  Strickland  are  especially 
recommended  to  pvi})ils  of  ten  or  twelve  years  of  age. 

In  respect  to  the  Arts,  the  pupil  should  learn,  during  this  period, 
to  write  a  good  hand,  t©  draw  with  considerable  skill,  to  read 
musie  by  note,  to  sing,  and  if  he  has  musical  talent,  to  play  one 
or  two  instruments.  Girls  should  learn  to  sew,  mend,  darn,  cut 
and  fit  garments,  and  receive  instruction  in  housekeeping,  cook- 
ing, etc.  Boys  skould  become  familiar  with  the  use  of  tools,  and 
acquire  some  of  the  elements  of  the  mechanic  arts.  If  there  is 
special  talent  for  the  niechanic  or  fine  arts,  an  opportunity  should 
be  aflTorded  for  additioaal  oulture  in  these  branches. 

Some  of  the  elements  of  Mental  and  Moral  Philosophy  might 
be  learned  during  this  period,  but  it  is  thought  that  any  formal 
study  of  these  branches  should  be  usually  postponed  until  after 
the  age  of  sixteen. 

Manhood. — During  this  period  the  Language  studies  of  the 
previous  period  should  be  continued  into  their  higher  depart- 
ments; in  addition  to  which  there  should  be  a  thorough  course 
in  Rhetoric,  Genesal  Literature,  Philology,  etc.     There  should 


THE    ORDER   OF   INSTRUCTION.  61 

also  be  an  extensive  course  of  general  reading  of  the  poets  and 
prose  writers,  and  a  close  and  careful  study  of  some  of  them  as 
models  of  style  and  expression.  There  should  also  be  much 
practice  in  composition,  and  the  pupil  should  become  a  good 
writer  and  speaker. 

The  Mathematical  studies  of  this  period  should  include 
higher  arithmetic,  higher  algebra,  higher  geometry,  trigonom- 
etry and  surveying,  analytical  geometry,  difierential  and 
integral  calculus,  and  the  philosophy  of  mathematics.  If 
there  is  time,  some  of  the  recently  developed  branches  of  the 
science  may  also  be  studied ;  and  the  pupil  should  be  encour- 
aged to  push  his  investigations  beyond  any  of  the  ordinary 
text-books  on  the  subject. 

The  course  in  Natural  Science  should  include  a  higher 
course  in  Natural  Philosophy,  embracing  mechanics,  optics, 
acoustics,  etc. ;  a  course  in  theoretical  and  practical  Astron- 
omy ;  a  full  course  in  Chemistry,  Anatomy,  and  Physiology; 
and,  if  possible,  quite  a  thorough  course  in  Natural  History. 
The  student  should  also  begin  the  investigation  of  the  facts 
and  phenomena  of  the  material  world  for  himself. 

The  course  in  History  should  include  the  reading  and  study 
of  a  complete  history  of  one's  own  country,  a  complete  course 
in  general  history,  a  careful  reading  of  the  detailed  history  of 
England,  France,  Gei-raany,  Spain,  etc.,  a  study  of  the  works 
on  the  philosophy  of  history,  as  Guizot,  Buckle,  Draper,  etc. 
The  effort  should  be  to  fix  permanently  in  the  mind  all  the 
great  and  leading  events  of  history,  and  to  learn  the  causes 
which  have  contributed  to  the  rise  and  fall  of  empires  and 
nations,  and  thus  to  learn  the  laws  w^hich  control  the  growth 
of  civilization. 

The  course  in  the  Arts  may  be  continued  for  a  year  or  two,  ac- 
cording to  the  taste  and  circumstances  of  the  pupil.  Girls  may 
continue  lessons  in  the  household  arts,  and  boys  may  acquire  con- 
siderable skill  in  working  in  wood  aud  iron.  When  there  is 
musical  taste,  it  may  include  the  culture  of  the  voice,  singing, 
instrumental    music,   thorough-bass,  musical    composition,   etc. 


62  METHODS  OF   TEACHING. 

When  there  is  taste  in  drawing,  it  may  include  sketching  from 
nature,  perspective  drawing,  painting,  etc.,  and  the  history  and 
philosophy  of  art.  Instruction  in  moulding  figures  out  of  clay 
or  plaster  will  be  valuable  to  both  boys  and  girls.  A  course  in 
Architecture  and  Landscape  Gardening  will  also  be  of  interest 
and  value  to  the  student  if  there  are  taste  and  time  for  it. 

The  student  is  now  prepared  tor  what  are  called  the  Meta- 
physical studies.  During  this  period,  he  should  take  a  course 
in  Mental  Philosophy,  Moral  Philosoph}^,  Logic,  Political 
Economy,  .Esthetics,  International  Law,  and  the  Evidences 
of  Natural  and  Revealed  Religion.  The  works  of  the  great 
thinkers,  Plato,  Aristotle,  Bacon,  Locke,  Kant,  Hegel,  Fichte, 
Hamilton,  and  the  writers  on  the  relation  of  modern  science 
to  philosephy  and  religion,  ma\'  be  studied.  Many  of  these 
studies,  however,  can  be  merely  begun  at  the  age  of  twenty- 
one,  and  should  be  continued  through  life. 

The  course  suggested  will  be  found  to  be  just  a  little  in 
advance  of  the  capacity  of  the  average  bo}^  and  girl,  as  we 
find  them  in  our  families  and  schools  ;_but  if  the  pupil  have  a 
careful  systematic  training  from  the  beginning,  he  will  be 
prepared  for  the  studies  named.  The  object  is  to  present  an 
ideal  of  what  the  course  should  be,  and  of  what  we  should  aim 
to  make  it. 


CHAPTER  X. 

THE   PRINCIPLES   OF   INSTRUCTION. 

rpHE  Principles  of  Instruction  are  the  laws  which  guide 
JL  the  teacher  in  imparting  instruction.  These  principles 
are  derived  from  three  distinct  sources ;  the  Nature  of  the 
Mind,  the  Nature  of  Knowledge,  and  the  Nature  of  In- 
struction. The  principles  derived  from  the  nature  of  the 
mind  have  reference  to  the  proper  culture  of  the  mental 
faculties  ;  those  derived  from  the  nature  of  knowledge  have 
reference  to  the  order  in  which  knowledge  shall  be  presented 
to  the  mind ;  and  those  derived  from  tlie  nature  of  instruction 
have  reference  to  the  manner  in  which  knowledge  shall  be 
taught.  We  shall  present  ten  principles  of  each  class,  which 
may  be  called  the  Teacher^s  Decalogue. 

Principles  Derived  from  the  Nature  of  Mind. 

The  following  ten  principles  are  derived  from  the  nature  ot 
the  mind,  and  indicate  the  laws  which  should  govern  the 
teacher  in  imparting  instruction  so  that  the  mind  may  be 
properly  trained  and  developed : 

1.  The  primary  object  of  teaching  is  to  afford  culture.  In  educa- 
tion culture  is  more  valuable  than  knowledge.  Culture  gives  the 
power  to  acquire  knowledge,  and  this  is  worth  more  to  the  pupil 
than  the  knowledge  he  has  already  acquired.  Culture  also  gives 
one  the  power  to  originate  knowledge,  to  invent  new  ideas  and 
thoughts.  Without  culture  the  mind  is  a  mere  receptacle  of  ideas 
and  tlioughts ;  with  it  the  mind  is  an  active  energy  that  can  trans- 
form its  knowledge  into  new  products.  Knowledge  makes  a 
learned  man ;  culture  m^ikes  a  wise  man ;  and  wisdom  is  better 
than  learning.     This  primary  object  of  teaching  should  never  be 

'(63) 


64  METHODS   OF   TEACHING, 

forgotten.  The  teacher  should  carry  in  his  mind  a  clear  conception 
of  the  faculties  of -his  pupils,  and  keep  constantly  before  him  the 
thought  whether  his  work  is  adapted  to  the  growth  and  culture 
of  these  faculties.  He  should  know  the  relation  of  each  branch 
of  study  to  the  minds  of  his  pupils,  see  clearly  what  faculties 
are  brought  into  activity  by  it,  and  be  sure  that  his  work  is 
giving,  not  merel}'  knowledge,  but  intellectual  power.  In 
other  words,  he  should  measure  his  work,  not  merely  b}'  the 
knowledge  he  is  imparting,  but  by  the  mental  power  he  is  cul- 
tivating. The  neglect  of  this  duty  has  warped  and  stunted 
man^'  a  3'onng  mind. 

2.  Exercise  is  the  great  law  of  culture.  This  law  is  univer- 
sal, applying  to  l)oth  mind  and  matter.  A  muscle  grows  strong 
by  exercise.  The  arm  of  the  blacksmith  and  the  leg  of  the 
pedestrian  acquire  size  and  power  by  use.  So  ever}-  faculty 
of  the  mind  is  developed  b}'  its  proper  use  and  exercise.  The 
power  of  perception  grows  by  perceiving,  the  power  of  mem- 
ory b}'  remembering,  the  power  of  thought  by  thinking,  etc. 
Hang  the  arm  in  a  sling  and  the  muscle  becomes  flabby  and 
almost  powerless  ;  let  the  mind  remain  inactive  and  it  acquires 
a  mental  flabbiness  that  unfits  it  for  any  severe  or  prolonged 
activity.  An  idle  mind  loses  its  tone  and  strength,  like  an 
unused  arm ;  the  mental  powers  go  to  rust  through  idleness 
and  inaction. 

3.  The  teacher  ahould  aim  to  give  careful  culture  to  the 
perceptive  powers  of  the  child.  The  perceptive  powers  are 
the  most  active  in  childhood.  Mental  activity  begins  in  the 
senses.  A  little  child  almost  lives  in  its  eyes  and  ears  and 
fingers;  it  delights  to  see  and  hear  and  feel.  Its  eyes  are 
sharp,  its  ears  are  quick,  and  its  fingers  so  busy  as  to  be  con- 
tinually in  what  people  call  "mischief."  The  teacher  shouhl 
direct  this  activity,  and  give  the  child  food  for  the  senses. 
He  should  provide  objects  for  its  instruction,  and  give  it  facts 
to  satisfy  this  craving  mental  appetite,  rather  than  attempt  to 
feed  it  upon  abstract  ideas  and  thoughts  for  which  it  has  no 
taste  or  capacity. 


THE    PRINCIPLES    OF    INSTRUCTION.  65 

4.  The  teacher  should  aim  to  furnish  the  memory  of  the 
child  with  facts  and  ivords.  Tlie  memory  of  children  is  es- 
pecially strong  for  facts  and  words.  Every  object  of  nature 
comes  through  the  senses  with  such  a  freshness  to  the  mind 
that  it  stamps  itself  indelibly  on  the  memory.  Facts  seem  to 
stick  as  naturally  to  the  young  mind,  as  burrs  to  the  dress. 
Its  memory  for  words  is  no  less  remarkable  than  its  memory  of 
things.  A  new  word,  once  heard,  is  usually  a  pernmnent  pos- 
session. A  child  will  learn  to  speak  three  or  four  languages 
in  a  year,  if  it  has  the  opportunity  of  doing  so.  The  teacher 
should  remember  these  fticts,  and  conform  his  work  to  them. 
He  should  give  the  child  an  opportunity  to  furnish  its  mind 
with  the  facts  of  nature  and  science,  and  also  to  add  to  its 
stock  of  words  and  acquire  a  rich  and  copious  vocabulary. 

5.  The  memory  should  be  trained  to  operate  by  the  laws  of 
association  and  suggestion.  The  mind  in  retaining  and  recall- 
ins:  knowledae  works  in  accordance  with  a  certain  law  of 
mental  operation.  It  ties  its  facts  together  by  the  thread  of 
association,  or  arranges  them  in  clusters  like  the  grapes  of  a 
buncn.  This  tendency  is  called  the  Law  of  Association.  The 
principal  laws  of  association  are  the  law  of  Similars,  the  law 
of  Contrast,  the  law  of  Cause  and  Effect,  and  the  law  of  Con- 
tiguity in  Time  and  Place.  The  teacher  should  understand 
these  laws  and  require  the  pupil  to  link  his  knowledge  together 
b}^  means  of  them.  In  geography  he  should  have  pupils  asso- 
ciate similar  facts  in  respect  to  cities,  states,  etc.;  in  history 
he  should  require  them  to  make  use  of  the  law  of  contiguit}'- 
in  time  and  place,  and  lead  them  to  associate  events  as  related 
by  cause  and  effect.  A.11  the  knowledge  taught  should  be  so 
systematized  that  it  may  be  readily  recalled  by  the  law  of 
logical  or  topical  relations. 

6.  The  power  of  forming  ideal  creations  should  be  carefully 
cultivated.  The  faculty  of  ideal  creation  is  the  Imagination. 
This  i)ower  is  awakened  into  action  through  the  medium  of 
perception.      The  facts  of  the  senses  touch  the  lancy,  ami 


d6  METHODS    OF   TEACHING. 

arouse  it  into  activity.  Tlie  forms  and  colors  of  nature,  the 
arching  skj^  and  the  spreading  landscape,  linger  in  the  mem- 
ory as  forms  of  beauty,  and  excite  the  imagination  to  modify 
aiid  create  such  forms  for  itself.  This  tendency  is  sometimes 
so  strong,  that  fact  and  fancy  })ecome  so  interwoven  in  tlie 
mind  of  a  child  that  it  is  ditlicnlt  to  discriminate  betwoon 
them.  The  teacher  should  encourage  the  activity  of  this 
faculty,  and  ti'ain  it  to  a  healthy  and  normal  development. 

7.  The  mind  should  he  gradually  led  from  concreie  to  ab- 
stract ideas.  The  young  mind  begins  with  the  concrete,  with 
olvjects  and  their  qualities.  Its  first  ideas  are  perce2:)tions  of 
objects,  of  things  that  it  can  see  and  hear  and  feel.  Its  ideas 
of  quality  are  not  abstracted  from,  but  rather  associated  with, 
objects.  These  concrete  qualities  it  begins  to  conceive  inde- 
pendently of  the  objects  in  which  they  are  found,  and  thus  it 
gradually  rises  to  abstract  ideas.  From  hard  objects  it  gets 
its  ideas  of  hardness,  from  kind  parents  and  friends  it  obtains 
its  notion  of  kindness,  etc.  This  natural  tendenc}'^  should  be 
noticed  and  aided,  so  far  as  possible,  by  the  teacher.  Espe- 
cially should  he  be  careful  not  to  lift  the  pui)il  up  into 
abstractions  too  soon.  He  should  present  concrete  exa,mples 
of  that  which  he  is  teaching,  that  the  pupil  may  have  a  defi- 
nite idea  of  the  subject  to  be  presented  before  he  attempts  to 
consider  it  abstractly.  He  should  aid  the  child  to  rise  from 
things  to  thoughts. 

8.  A  child  should  be  gradualhj  led  from  particular  ideas  to 
general  ideas.  The  young  mind  begins  with  the  particular. 
Its  first  idea  is  of  particular  objects,  not  of  general  notions, 
A  man,  to  the  3^oung  mind,  is  a  particular  person;  a  bird  is  a 
particular  bird.  Gradually  it  rises  from  the  particular  object 
to  the  general  conception,  from  a  percept  to  a  concept.  Tlie 
teacher  should  watch  this  natural  tendcnc}'  and  aid  it.  The 
process  should  not  be  forced,  it  should  not  be  attempted  too 
earlj';  but  when  the  pupil  is  ready,  he  can  gradually  be  lifted 
lip  from  the  concrete  into  tlie  s])licre  of  abstract  and  general 


THE   PRINCIPLES    OF   INSTRUCTION.  67 

conceptions.     It  should  be  tlie«special  aim  of  the  teacher  to 
aid  the  mind  in  rising  from  the  particular  to  the  general. 

9.  A  child  should  be  taught  to  reason  first  inductively  and 
then  deductively.  The  child's  first  thoughts  are  the  facts  of 
sense.  From  these  particular  facts  it  gradually  rises  to  gen- 
eral truths.  By  and  by,  after  the  mind  has  attained  to  some 
general  principles  through  Induction,  it  begins  to  reverse  the 
process  and  infer  particular  truths  from  such  general  princi- 
ples. It  also  begins  to  apply  the  self-evident  truths  to  reach- 
ing conclusions  that  grow  out  of  them.  This  natural  activity 
of  the  mind  should  be  understood  by  the  teacher,  and  the  work 
of  instruction  be  done  accordingh'.  Especial  care  should  be 
taken  not  to  require  deductive  thought  too  early.  In  all  things 
the  law  of  nature  should  be  implicitly  followed. 

10.  A  child  should  be  gradually  led  to  attain  clear  concep- 
tions of  the  intuitive  ideas  and  truths.  Mental  life  begins  in 
the  senses ;  the  child's  first  ideas  and  truths  are  those  which 
relate  to  the  material  world.  But,  by  and  by,  intuition  awak- 
ens into  activity,  and  in  it  begin  to  dawH  the  ideas  and  truths 
of  the  Reason.  The  teacher  should  watch  this  natural  activit}'^, 
and  be  governed  by  it.  He  may  aid  the  child  in  developing 
the  ideas  of  Space,  Time,  Cause,  the  True,  the  Beautiful,  and 
the  Good,  by  presenting  suitable  occasions.  He  may  also  aid 
the  pupil  in  reaching  the  self-evident  truths  which  spring  out 
of  these  several  ideas,  by  particular  examples  and  suitable 
qiiestions.  Some  of  the  axioms  of  number  and  space  are  quite 
early  awakened  in  the  mind ;  and  the  teacher  can  aid  their 
development. 

Principles  Derived  from  the  Nature  of  Knowledge. 

The  principles  of  the  first  class  are  drawn  from  a  considera- 
tion of  tlie  nature  of  the  mind.  The  principles  of  the  second 
class  are  derived  from  the  consideration  of  the  nature  of 
knowledge.  The  following  ten  principles  are  regarded  as 
among  the  most  important: 


68  METHODS    OF    TEACHING. 

1.  The  second  object  of  teacJy,tig  is  to  imparl  knowledge,  a 
person  sliould  not  only  know  how  to  obtain  knowledge,  but 
he  should  possess  knowledge.  He  should  not  only  know  how 
to  use  his  memory  in  acquiring  knowledge,  but  he  should  have 
it  stored  with  interesting  and  useful  facts.  He  should  not  only 
know  how  to  think,  but  his  mind  should  be  filled  with  facts 
and  truths  both  as  the  materials  for  and  the  results  of  thought. 
Though  culture,  which  trains  to  the  use  of  the  faculties,  may 
be  better  than  learning,  learning  is  very  much  better  than 
ignorance.  The  teacher  should  therefore  aim  to  fill  the  minds 
of  his  pupils  with  the  tacts  of  history,  geography,  natui'al 
science,  etc.  He  should  hold  up  before  them  a  high  ideal  of 
scholarship,  and  create  in  them  an  ambition  for  wide  and 
extensive  learning. 

2.  Things  should  he  taught  before  ivords.  This  principle  is 
in  accordance  with  the  natural  development  of  knowledge. 
The  object  existed  and  was  known  before  a  name  was  given 
to  it;  the  word  was  introduced  to  designate  the  object.  This 
natural  order  in  the  genesis  of  knowledge  should  be  folloAved 
in  the  imparting  of  knowledge.  The  principle  is  also  in 
accord  with  the  natural  laws  of  mental  development. 

This  principle  is  very  frequently  disregarded  by  the  teacher. 
It  is  violated  by  requiring  pupils  to  commit  words  without 
definite  ideas  of  their  meaning,  and  to  repeat  definitions  with- 
out understanding  them.  Such  a  course  is  most  pernicious 
in  its  influence  on  the  mind.  It  leads  the  pupil  to  acquire 
wrong  habits  of  thought,  to  be  satisfied  with  the  expression 
without  a  knowledge  of  the  idea  or  fact  expressed ;  and  deludes 
him  with  the  idea  that  words,  the  symbols,  are  the  realities  of 
knowledge. 

3.  Ideas  should  be  taught  before  truths.  This  law  is  also  iii 
accordance  with  the  natural  law  of  acquisition  and  mental 
development.  The  mind  has  ideas  before  it  puts  them  to- 
gether in  judgments  or  thoughts.  Thus  it  has  an  idea  of  a 
chair  and  the  ^oor  before  it  thinks  the  chair  is  on  the  floor 


THE   PRINCIPLES   OF   INSTRUCTION.  69 

So  iu  science,  as  in  aritlimetic  and  geometry,  the  ideas  pre- 
sented in  the  definitions  are  learned  before  the  truths  which 
pertain  to  them.  This  principle  is  also  manifest  from  the  na- 
ture of  the  mind.  Ideas  are  given  b}'  perception  and  concep- 
tion; thoughts  are  the  result  of  judgment  and  reasoning;  and 
the  acts  of  perception  and  conception  precede  those  of  judg- 
ment and  reasoning.  This  order  should  be  followed  in 
instruction.  The  effort  of  the  teacher  should  be  to  fill  the 
mind  of  the  pupil  with  ideas,  both  concrete  and  abstract,  and 
subsequently  to  teach  the  truths  which  belong  to  them. 

4.  Particular  ideas  s/wuld  be  taught  before  general  ideas. 
This  principle  is  in  accordance  with  the  genesis  of  knowledge 
and  the  natural  activity'  of  the  mind.  Our  first  ideas  are  of 
particular  objects,  derived  through  the  senses;  following  these 
come  the  abstract  and  general  notions  given  b}^  the  under- 
standing. •  Thus  a  child  has  an  idea  of  a  particular  bird  before 
it  can  conceive  of  a  bird  in  general,  or  of  a  class  of  birds ;  and 
the  same  is  true  of  other  notions.  This  order,  fre([uently 
violated  in  education,  should  be  carefully  followed.  To  depart 
from  it  is  to  invert  the  law  of  mental  activity  and  injure  the 
mind,  as  well  as  retard  the  acquisition  of  knowledge.  The 
motto  should  be, — from  the  particular  notion  or  idea  to  the 
general. 

5.  Facts^  or  particular  truths,  should  be  taught  before  prin- 
ciples, or  general  truths.  A  fact  is  a  truth  in  the  domain  ui 
sense;  a  principle  is  a  truth  in  the  domain  of  thought.  The 
former  is  concrete;  the  latter  is  abstract;  and  the  concrete 
should  be  taught  before  the  abstract.  The  former  results  from 
an  operation  of  perception  and  judgment;  the  latter  from  an 
act  of  reasoning;  and  an  act  of  perception  precedes  an  act  of 
reasoning.  Again,  facts  are  particular  truths;  principles  are 
ger.eral  truths;  and  the  particular  should  precede  the  general. 
The  principles  in  natural  science  are  a  generalization  from 
facts;  and  the  mind  must  be  familiar  with  the  facts  before  it 
can  generalize  from  them.     It  is  thus  clear  that  facts,  or  par- 


70  METHODS    OF    TEACHINQ. 

ticuliir  truths,  should  be  taught  before  i3rinci2:)les,  or  general 
truths. 

6.  In  the  physical  sciences  causes  should  be  taught  before 
laws.  In  the«i)hysical  sciences  we  proceed  tVora  facts  and 
phenomena  to  the  laws  and  causes  relating  to  them.  In  pre- 
senting these,  the  law  of  mental  growth  indicates  that  we 
should  teach  the  causes  of  things  before  presenting  their  laws. 
The  idea  of  cause  is  very  early  awakened  in  the  mind.  One 
of  the  first  questions  of  a  little  child  is,  "  Mamma,  what  makes 
that?"  The  ascertaining  of  the  laws  wliich  control  facts  and 
phenomena  is  a  later  consideration.  The  same  conclusion 
appears  from  the  genesis  of  knowledge.  The  causes  of  physi- 
cal phenomena  were  sought  for  long  before  an  inquiry  was 
made  for  their  laws.  The  ancients  early  made  inquiiies  after 
the  causes  in  natural  philosophy  and  astronomy ;  the  attempt 
to  ascertain  the  laws  is  of  much  more  recent  date.  Besides, 
too,  the  law  often  flows  from  a  correct  idea  of  the  cause,  as  in 
gravitation,  optics,  etc.  It  is  thus  clear  that  in  teaching  the 
ph^'sical  sciences,  the  causes  of  facts  should  be  considered 
before  their  laws. 

T.  In  the  physical  sciences,  causes  and  laws  should  he  taught 
before  the  scientific  classific<ations.  This  is  indicated  by  the 
law  of  menital  growth,  and  also  by  the  genesis  of  the  sciences. 
The  mind  grasps  facts,  causes,  and  laws,  before  it  is  ready  for 
the  grand  generalizations  of  Natural  Histor3^  These  latter 
require  a  knowledge  of  particulars  and  a  breadth  of  conception 
entirely  beyond  the  grasp  of  the  young  mind.  The  order  of 
development  of  these  sciences  also  indicates  the  same  law. 
The  scientific  classifications  of  Natural  History  are  much 
more  recent  than  the  facts  and  principles  of  Natural  Philoso- 
ph}:.  Astronomy,  etc. 

8.  The  elements  of  the  Inductive  Sciences  should  precede 
the  Deductive  Sciences.  The  elements  of  the  Inductive  Sciences 
are  facts  and  phenomena;  from  these  we  proceed  by  inductive 
reasoning  to  laws,  causes,  and  S3^steras  of  classification.    These 


THE    PRINCIPLES    OF    INSTRUCTION.  71 

facts  and  phenomena  are  acquired  by  perception,  and  may 
thus  be  early  presented  to  the  learner.  The}^  come  naturally 
into  the  mind  before  the  ideas  of  the  Deductive  Sciences,  and 
should  therefore  be  taught  before  them.  It  is  only  the  ele- 
ments of  these  sciences,  however,  that  should  precede  the 
deductive  sciences.  The  reasoning  of  the  inductive  sciences, 
by  which  we  attain  the  laws,  causes,  etc.,  is  more  difficult 
than  the  first  steps  of  reasoning  in  the  deductive  sciences ; 
and  should  not,  except  in  its  simplest  form,  be  taught  so 
early. 

9.  The  formal  study  of  the  Deductive  Sciences  should  pre- 
cede that  of  the  Inductive  Sciences.  This  order  arises  from  the 
nature  of  knowledge  in  its  relation  to  the  mind.  Though  the 
elementary  facts  of  the  inductive  sciences  present  themselves 
to  the  mind  as  early  as  the  elementary  ideas  of  the  deductive 
sciences,  yet  the  first  steps  of  formal  reasoning  in  the  deduct- 
ive sciences  are  simpler  than  those  of  the  inductive  sciences. 
Thus,  the  acts  of  judgment  in  Mental  Arithmetic,  and  the 
S3dlogisms  of  Geometry',  are  much  more  readily  grasped  by 
the  3'oung  mind  than  the  generalizations  of  Botany,  or  the 
investigati^ons  of  Xatural  Philosophy. 

Besides,  the  reasoning  in  the  mathematical  sciences  trains 
the  mind  to  see  the  relation  of  premise  and  conclusion,  and 
gives  it  the  habit  of  logical  activity.  A  mind  brought  up  on 
facts,  without  the  training  of  arithmetic  and  geometry,  will 
be  weak  and  illogical  in  its  operations,  and,  as  a  rule,  incom- 
petent for  profound  thinking.  The  fact  that  mathematics  and 
logic  were  developed  before  the  natural  sciences  also  indicates 
the  correctness  of  this  principle.  The  fact,  also,  that  many 
of  the  physical  sciences,  as  Xatural  Philosophy  and  Astron- 
omy, cannot  be  developed  without  the  aid  of  mathematics, 
makes  the  order  stated  in  the  principle  a  practical  necessity 
in  respect  to  those  branches. 

10.  The  Jfetaphysical  Sciences  should  be  the  last  in  a  course 
of  instruotion.     The  term    metaphysical    is    here   used    in  a 


'72 


METHODS   OF   TEACHING. 


general  sense,  to  include  Psj'chology,  Logic,  Ethics,  Esthet- 
ics, etc.  These  branches  are  the  most  abstract  in  their 
nature,  and  require  the  most  maturity  of  thought  for  their 
comprehension.  They  are  the  product  of  profound  reflection 
and  of  that  ripeness  of  wisdom  which  comes  with  the  maturity 
of  age  and  study;  and  as  such  should  not  be  entered  upon 
until  the  pupil  has  attained  considerable  maturity  of  mind 
and  culture. 

Principles  Derived  from  the  Nature  of  Instruction. 

The  first  and  second  classes  of  principles  are  drawn  from 
the  first  and  second  elements  of  the  problem  of  education, — 
the  nature  of  mind  and  the  nature  of  knowledge.  The  third 
class  is  derived  from  the  third  element  of  this  problem, — the 
nature  of  instruction.  We  giv«  the  following  ten  principles 
as  among  the  most  important : 

1.  Primary  Instruction  should  proceed  from  the^known  to 
the  unknown.  A  pupil  should  begin  to  learn  the  new  just 
where  his  knowledge  of  the  old  ends.  He  should  be  led  to 
understand  the  new  by  seeing  its  relation  to  the  old,  and,  if 
possible,  its  method  of  development  from  it.  The  known 
should  be  the  stepping-stone  to  the  unknown.  What  the 
child  knows  should  be  the  liarht  in  which  he  is  to  see  and 
understand  that  which  he  is  to  know.  The  elements  of  even 
the  higher  branches  should  be  taught  in  this  way.  Algebra 
should  begin  in  arithmetic,  analytical  geometry  in  algebra  and 
geometry,  etc.  This  principle  was  first  announced  b}'  Aris- 
totle, and  is  one  of  the  most  important  in  the  science  of 
teaching. 

2.  Advanced  Instruction  may  sometimes  proceed  from,  the 
unknown  to  the  knour/i.  A  pupil  ma}'  sometimes  fix  in  his 
memory  what  he  does  not  understand,  and  afterward  obtain  a 
clear  idea  of  it.  A  definition  ma}-  sometimes  be  committed 
to  memory  before  its  meaning  is  understood.  An  unknown 
hypothesis  is  often  assumed  in  an  investigation,  from  which 


THE   PRINCIPLES   OF   INSTRUCTION.  73 

\re  trace  our  way  to  known  facts.  A  law,  or  method  of 
operation,  whose  relation  to  the  known  is  not  at  present 
understood,  may  be  accepted  as  correct,  with  the  expectation 
that  the  future  will  make  it  clear  to  the  mind.  It  is  in  this 
manner  we  reason  in  algebra  by  tracing  our  way  from  the 
unknown  to  the  known;  and  the  same  method  is  sometimes 
used  in  geometry.  We  should,  therefore,  sometimes,  in 
teaching  and  in  study,  proceed  from  the  unknown  to  the 
known. 

3.  Primary  Instruction  should  be  given  in  the  concrete.  All 
primary  instruction  should  begin  in  the  concrete.  Knowledge 
at  first  must  pass  through  the  senses  into  the  mind.  The 
child  must  go  from  things  to  ideas  and  thoughts.  The  child's 
first  lesson  in  numbers  should  be  given  with  objects.  The 
measures  of  denominate  numbers  should  be  presented  so  that 
when  pupils  talk  of  gills,  pints,  etc.,  they  may  have  definite 
ideas  of  them.  The  things  defined  in  geography  —  capes, 
bays,  isthmuses,  etc. — should  be  learned  through  pictures  or 
by  means  of  some  tangible  representation  of  them.  The  ele- 
mentary ideas  of  geometry  are  to  be  taught  by  diagrams  and 
models,  and  the  truth  should  be  presented  at  first  by  concrete 
illustrations.  From  these  dmcrete  ideas  the  pupils  can  grad- 
ually pass  to  the  higher  abstractions  of  the  several  sciences. 

4.  Advanced  Instruction  should  be  more  abstract.  The 
mind  at  first  uses  the  concrete  thing  to  aid  it  in  rising  to  the 
abstract  thought.  At  first  it  hobbles  along,  as  it  were,  on  the 
crutches  of  sense ;  but  at  last  its  wings  become  plumed,  and 
it  can  soar  unaided  in  the  higher  atmosphere  of  abstraction. 
The  concrete  is  then  no  longer  needed  ;  the  thought  is  grasped 
without  the  illustration  or  representative  object.  Concrete 
instruction  should  therefore  not  be  continued  too  long.  To  de- 
pend always  upon  the  thing  for  the  thought  will  be  to  weaken 
the  mind  and  lower  its  appreciation  of  the  pure  ideas  of  science. 
To  teach  moral  philosophy  with  apples  and  potatoes  is  a  deg- 
radation of  truth,  as  well  as  a  source  of  weakness  in  mental 

4 


74  METHODS   OF   TEACHING. 

culture.     The  mind  o^rows  stronsr  in  its  wrestlins:  with  and 
its  grasp  of  the  principles  of  abstract  truth. 

5.  Primary  Instruction  should  be  both  analytic  and  synthetic. 
Some  subjects  should  be  presented  anal^'tically  and  others 
synthetically;  and  in  many  subjects,  both  methods  should  be 
combined.  In  teaching  reading,  we  begin  with  words,  then 
unite  these  into  sentences,  and  afterward  analyze  them  into 
their  letters.  Pronunciation  also  proceeds  by  analj'sis  and 
synthesis  ;  first  a  synthesis  of  the  sounds  in  the  word,  then 
the  analysis  of  the  word  into  its  elements,  and  then  again  the 
synthesis  of  he  elements  into  words.  Grammar  should  be 
taught  first  synthetically  and  then  analytically,  and  then  the 
two  methocls  should  be  united.  In  geography  we  would  begin 
with  the  elements  found  in  and  around  the  school-house,  pass 
out  to  the  fields  and  farms,  the  map  of  the  township,  etc., 
which  is  synthetic  ;  and  then  subsequentl}'  begin  at  the  world 
as  a  whole,  and  come  down  by  analysis  to  the  details  of  the 
subject.  In  primary  arithmetic  we  begin  with  synthesis,  but 
in  a  short  time  we  begin  to  reverse  the  process  and  proceed 
also  by  analysis.  Thus  addition  precedes  subtraction,  multi 
plication  comes  before  division,  etc.;  and  an  arithmetical  solu- 
tion contains  both  analysis  and  synthesis. 

6.  Advanced  Instruction  should  be  both  analytic  and  si/n- 
thetic.  Some  of  the  advanced  studies  should  be  presented 
analytically  and  some  synthetically ;  and  often  the  two  are 
united  in  different  degrees  in  dilTerent  parts  of  the  same 
study.  In  one  class  of  studies,  anah^sis  seems  to  precede  and 
synthesis  to  follow ;  in  another  class,  this  order  is  reversed. 
In  the  natural  sciences,  the  pupil  should  be  led  to  analyze  for 
the  elements,  and  afterwards  to  synthetize  these  into  the 
science  :  facts  are  to  be  put  together  into  classes,  and  phenom- 
ena to  be  combined  so  as  to  reach  their  laws  and  causes.  In 
the  mathematical  sciences,  the  lower  stage  seems  more  syn- 
thetic, and  the  higher  stage  more  analj^tic:  the  advance  is 
from    arithmetic    to   algebra,   from   the    ordinar}'    synthetic 


THE   PRINCIPLES    OF   INSTRUCTION.  75 

geometry  to  the  higher  analytical  geometry,  from  plane  trigo- 
nometry to  analytical  trigonometry,  from  synthetic  mechanics 
to  analytical  mechanics,  etc.  The  tendency  of  all  the  highei 
studies  is  towards  the  analytical  methods  of  thought  and  in- 
yestigation. 

7.  Primary  Instruction  should  be  inductive.  Little  chil- 
dren should  be  led  from  particulars  to  generals.  They  should 
proceed  from  special  examples  to  general  rules  or  laws  which 
embrace  them.  In  arithmetic,  they  should  learn  particular 
solutions  before  they  learn  a  general  rule  ;  and  be  required 
also  to  derive  the  general  rules  from  the  solution  of  particular 
cases.  In  grammar  they  should  learn  the  general  laws  of 
speech  by  first  seeing  them  presented  in  particular  instances. 
In  geograph}^  they  should  know  the  detailed  facts  before  they 
begin  to  generalize  them  into  classes  and  inquire  after  their 
laws  and  causes.  So  in  learning  the  definitions  of  any  branch, 
pupils  should  be  familiar  with  the  idea  to  be  defined  before 
they  attempt  to  express  it  in  a  definition.  Definitions  when 
stated  in  the  inductive  form  are  more  appropriate  to  young 
pupils,  than  when  presented  in  the  deductive  form. 

8.  Advanced  Instruction  should  be  deductive.  "With  ad- 
vanced pupils  the  deductive  method  is  preferred.  They 
should  be  taught  to  reason  from  general  principles.  They 
should  be  required  to  grasp  general  laws  of  a  subject  and 
apply  them  to  particular  cases.  In  mathematics,  the  demon- 
strative method  of  reasoning  should  be  employed.  Thus,  in 
fractions,  the  rules  for  all  the  various  cases  may  be  derived 
from  the  principles  of  fractions.  In  geography,  the  classifica- 
tion of  the  facts  should  be  learned,  and  their  causes  and  laws 
explained,  as  we  have  them  treated  in  Physical  Geography. 
The  fundamental  principles  of  grammar  are  to  be  understood, 
and  to  be  applied  in  correcting  and  constructing  language. 
In  higher  mathematics,  we  should  proceed  from  the  compre- 
hending principle  to  the  truths  contained  in  it.  La  Grange, 
in  his  great  work  on  mechanics,  puts  the  whole  doctrine  of 


76  METHODS   OF   TEACHING. 

the  phj'sical  universe  into  an  equation,  and  unfolds  the  sci. 
ence  of  mechanics  b}'  a  discussion  of  this  equation ;  and  thi3 
is  the  spirit  of  the  modern  system  of  mathematics. 

9.  Primary  Instruction  should  proceed  from  the  practical 
to  the  theoretical.  Young  pupils  should  be  drilled  in  doing 
rather  than  in  thinking.  In  arithmetic,  the^'  should  have 
abundant  j)ractice,  and,  at  first,  but  little  theory  :  thej'^  should 
be  drilled  in  doing  the  work,  and  not  iu  explaining  it.  In 
reading,  the  drill  should  be  in  the  art  of  expression,  rather 
than  on  the  principles  of  elocution.  In  grammar,  the  primary' 
object  should  be  to  teach  pupils  to  use  correct  language, 
rather  than  to  understand  the  principles  of  grammatical  con- 
struction. The  practice  of  rhetoric  should  precede  its  study 
as  a  science.  The  pupil  should  know  how  to  think  before  he 
studies  logic,  the  science  of  thought.  From  a  correct  prac- 
tice in  these  branches  they  can  be  led  to  the  laws  which 
govern  this  ]^ractice. 

10.  Advanced  Instruction  should  proceed  from  the  theoret- 
ical to  the  practical.  While  younger  pupils  depend  on  imita- 
tion for  their  practice,  advanced  pupils  should  be  required  to 
derive  their  practice  from  principles.  They  will  thus  see  the 
reason  for  their  practice,  and  be  able  to  direct  it  independ- 
ently of  the  teacher  or  text-book.  In  arithmetic,  they  should 
be  required  to  give  a  reason  for  the  method  used,  and  present 
a  logical  explanation  of  their  work.  In  grammar,  the  princi- 
ples which  govern  the  construction  of  a  sentence  should  be 
clearly  understood,  and  the  pupil  should  endeavor  to  guide 
his  practice  by  these  theoretical  principles.  In  algebra,  there 
should  be  a  discussion  of  the  theoretical  principles  of  the 
science,  as  well  as  a  solution  of  problems  ;  and  the  science  of 
geometry  should  precede  the  practice  of  surveying.  A  mind 
educated  onl}^  in  practice  will  never  know  anj'thing  but  prac- 
tice ;  a  mind  familiar  with  principles  can  originate  and  direct 
his  practice  as  the  circumstances  may  require. 


PART  II. 

TEACHING  THE  BRANCHES. 


I.    OBJECT  LESSONS. 


II.    TEACHING  LANGUAGE. 


IIL    TEACHING  MATHEMATICS. 


IV.    TEACHING  PHYSICS. 


V.    TEACHING  HISTORY 


OBJECT    LESSONS. 


CHAPTER  I. 

THE   NATURE   OF    OBJECT   LESSONS. 

OBJECT  LESSONS  are  lessons  designed  to  give  elemen- 
tary cnlture  and  instruction  by  means  of  objects.  They  are 
designed  to  afford  that  culture  to  the  young  mind  which  se- 
cures a  natural  development  of  its  faculties,  and  also  to  im- 
part a  knowledge  of  the  elementary  facts  and  principles  of 
all  the  sciences. 

Such  lessons  have  been  introduced  into  nearly  all  our 
schools,  and  are  regarded  as  an  essential  part  of  a  system  of 
primary  instruction.  The  credit  of  introducing  Object  Les- 
sons, as  a  distinct  method  of  elementary  instruction,  has 
been  attributed  to  Pestalozzi;  though  Locke,  Comenius,  and 
others  advocated  such  instruction  before  him.  In  fact,  the 
principle  of  Object  Lessons  is  as  old  as  instruction  itself;  for 
all  good  teachers  have  used  objects  in  illustration  of  abstract 
subjects.  We  shall  consider  briefly  their  Value,  the  Prepara- 
tion required,  the  Method  of  giving  an  object  lesson,  the 
Errors  to  be  avoided,  and  the  Course  of  Instruction;  and  then 
present  outlines  and  remarks  to  suggest  a  practical  course  to 
the  young  teacher. 

Value  of  Object  Lessons — A  system  of  Object  Lessons 
is  of  great  value  in  education.  Their  object,  as  already  stated, 
is  two-fold ;  to  give  both  culture  and  instruction  to  the  young 
mind. 

(79) 


80  METHODS   OF   TEACHING. 

Object  Lessons  cultivate  the  Perceptive  Powers.  Objects  are 
presented  requiring  pupils  to  observe  their  form,  color,  quali- 
ties, etc.,  and  thus  the  powers  of  perception  are  exercised  and 
developed.  An  object  lesson  requires  a  pupil  to  analyze  an 
object  carefully  into  its  parts,  to  look  at  its  details  ;  and  this 
leads  a  pupil  to  acquire  the  habit  of  close,  accurate,  and  ana- 
lytical perception. 

Object  Lessons  give  culture  to  the  Memory.  Names  of  ob- 
jects, their  parts,  qualities,  etc.,  are  to  be  remembered  and 
recalled.  This  knowledge  being  presented  in  a  concrete  form 
makes  a  much  deeper  impression  upon  the  memorj%  and  is 
thus  more  readily  fixed  in  the  mind.  Besides,  the  knowledge 
communicated  is  that  which  is  required  by  the  young  mind,  a 
knowledge  of  objects  and  facts,  rather  than  of  abstract  ideas 
and  truths;  and  is  thus  adapted  to  give  normal  exercise  and 
culture  to  the  faculty  of  the  memory. 

Object  Lessons  give  culture  to  the  Imagination.  They 
give  definite  pictures  to  the  representative  power  as  recalled 
by  memory,  and  thus  excite  the  imagination  to  create  ideal 
images.  The  memory  may  be  filled  with  beautiful  pictures  of 
nature  which  become  the  type  after  which  the  imagination 
creates  its  ideals.  A  system  of  object  lessons,  thus  operating 
through  the  memory,  may  become  a  source  of  rich  culture  to 
the  imagination. 

Object  Lessons  give  culture  to  the  Judgment.  Pupils  are 
taught  to  compare  one  object  with  another  and  determine  their 
relations.  The  colors  of  objects  are  compared  with  standard 
colors  ;  the  sizes  of  objects  are  determined  from  their  relation 
to  fixed  standards  of  size  ;  the  length  and  breadth  of  rooms, 
the  height  of  ceilings,  etc.,  are  estimated  and  expressed  \n  dif- 
ferent units  ; — all  of  which  give  exercise  to  the  judgment,  and 
thus  strengthen  and  develop  it. 

Object  Lessons  give  culture  to  the  Attention.  The  mind  ot 
the  pupil  is  aroused  and  attracted  by  the  object  and  is  thus 
concentrated  upon  it.     The  propensity  of  the  mind  of  a  child 


THE    NATURE    OF    OBJECT   LESSONS.  81 

to  wander  from  one  thing  to  another  is  thus  cliecked,  and  the 
habit  of  mental  concentration  formed.  The  power  of  atten- 
tion is  thus  largely  exercised  and  cultivated  by  a  system  of 
object  lessons. 

Object  Lessons  are  especially  adapted  to  give  culture  in  the 
use  of  Language.  They  impart  new  words  as  names  of 
objects,  qualities,  etc.,  which  become  fixed  in  the  memory  and 
enrich  the  pupil's  vocabulary.  They  also  give  pnpils  practice 
in  talking,  by  telling  what  they  see  or  have  learned.  They 
especially  cultivate  the  habit  of  using  words  as  expressing 
definite  ideas,  and  thus  lead  to  precision  and  accuracy  in  the 
use  of  language. 

Object  Lessons  train  to  habits  of  definite  and  accurate  con- 
ception. Knowledge  is  most  readily  conveyed  to  the  mind 
through  the  medium  of  the  eye.  "  Seeing  is  believing  "  is  an 
old  adage  which  indicates  the  exactness  of  the  knowledge 
which  we  gain  through  the  sense  of  vision.  Such  definite  per- 
ceptions train  the  mind  to  the  habit  of  definite  conceptions, 
of  conceiving  ever3^thing  with  exactness  and  completeness.  A 
mind  thus  trained  is  not  satisfied  with  the  misty  and  shadowy 
conceptions  which  often  pass  for  knowledge. 

Object  Lessons  are  of  value  in  imparting  Knoivledge  to  the 
mind.  By  means  of  object  lessons,  the  elements  of  nearly 
all  the  different  sciences  may  be  presented  to  children.  Thus 
the  elements  of  geometry  may  be  taught  by  diagrams  cut  from 
pasteboard.  The  elements  of  arithmetic  may  be  presented  by 
means  of  objects  and  the  numeral  frame.  By  means  of  speci- 
mens of  plants  and  insects,  by  charts,  cards,  etc.,  the  elements 
of  botany,  zoology,  etc.,  may  be  imparted.  A  system  of 
object  lessons,  can,  therefore,  be  so  arranged  as  to  give  pupils 
a  knowledge  of  the  elementary  facts  of  nearly  all  the  sciences. 
Such  a  knowledge  will  prove  of  great  value  to  them  when,  in 
after  years,  they  are  prepared  to  study  these  branches  as 
sciences. 

The  instruction  in  the  elements  of  the  physical  sciences^ 
4* 


82  METHODS   OF   TEACHING. 

as  botany,  physiology,  etc.,  will  be  of  special  value  to  the 
pupils  of  our  public  schools.  Without  such  instruction,  man}'- 
of  them  will  go  out  and  become  citizens,  ignorant  of  the  sim- 
plest facts  and  principles  of  these  sciences,  for  they  cannot  be 
expected  to  study  them  from  a  text-book  in  the  ordinary 
common  school.  With  charts  and  suitable  specimens,  a  fair 
knowledge  of  the  fundamental  facts  of  ph^-siology  can  be  given 
in  a  few  weeks,  knowledge  absolutel}-  essential  to  the  healtL 
and  happiness  of  mankind.  In  a  similar  manner,  pupils 
may  be  made  familiar  with  many  of  the  principal  facts  of 
botany,  natural  philosophy,  chemistry,  etc. 

Preparafion  for  Object  Lessons. — Under  the  Prepara- 
tion for  Object  Lessons  we  shall  speak  of  the  Preparation  of 
Material,  the  Preparation  of  the  Teacher,  and  the  Preparation 
of  the  Pupil. 

Prepa)-ation  of  Material. — Ever}-  school  should  be  provided 
with  objects  suitable  for  giving  object  lessons.  There  should 
be  a  collection  of  specimens  of  leaves,  flowers,  minerals,  bones, 
all  the  ordinary  grains,  specimens  of  wood,  insects,  coins,  etc. 
Every  school  should  be  provided  with  a  cabinet  in  which  these 
objects  are  to  be  placed  and  preserved.  There  should  also  be 
charts  of  colors,  of  geometrical  figures,  of  animals  and  plants, 
etc.  Besides  these,  there  should  be  some  apparatus  in  the 
public  schools,  to  illustrate  the  elementar}'  facts  and  princi- 
ples of  natural  philosophy  and  chemistry.  Every  school 
should  possess  a  glass  prism,  a  magnet,  a  microscope,  a 
galvanic  battery,  an  electrical  machine,  etc.  There  are  many 
little  things  which  a  teacher  can  make,  or  procure  with  very 
slight  expense,  such  as  a  siphon,  a  tube  for  pneumatics,  etc.; 
and  a  live  teacher  can  raise  the  money  among  his  patrons 
to  procure  many  of  the  things  mentioned. 

Preparation  of  the  Teacher. — The  teacher  should  prepare 
himself  with  information  upon  these  objects.  This  he  can  do 
by  observation,  conversation,  and  reading.  By  visiting  shops, 
stores,  mills,  etc.,  he  will  be  able  to  gain  a  great  deal  of  valua- 


THE   NATURE    OF    OBJECT   LESSONS.  83 

ble  knowledge  of  objects  and  common  things  which  he  can 
use  in  giving  object  lessons.  He  should  also  consult  ency- 
clopedias and  other  works  of  general  information.  In  gixing 
lessons  on  the  elements  of  the  different  sciences,  as  geometry, 
phj^siology,  botany,  etc.,  he  can  select  the  facts  he  needs  from 
the  text-books  on  these  subjects. 

The  teacher  should  also  prepare  himself  upon  the  method, 
as  well  as  upon  the  matter  of  an  object  lesson.  He  should 
systematize  his  knowledge,  and  arrange  it  in  the  order  in 
which  it  is  to  be  presented.  An  outline  should  be  prepared; 
and,  if  there  is  time,  committed  to  memory,  so  that  the  lesson 
ma^'  not  be  loose  and  rambling,  but  have  a  system,  and  be  di- 
rected toward  a  definite  end. 

Preparation  of  the  Pupil. — The  pupil  should  also  be  re- 
quired to  prepare  for  the  lesson.  He  should  first  be  required 
to  observe  all  he  can  of  an  object,  that  he  may  have  an  oppor- 
tunity for  the  culture  of  his  perceptive  powers.  He  ma^^  then 
make  inquiries  of  older  persons,  and  gain  what  information 
he  can  from  them.  Lastly,  he  may  go  to  books  treating  of 
the  subject,  and  learn  the  recorded  observations  of  others 
This  last  method  is  usually  the  easiest ;  and  care  should  be 
taken  that  the  pupil  does  not  resort  to  it  first,  and  thus, 
though  he  may  obtain  knowledge,  lose  the  primary  object  of 
the  lesson, — the  culture  of  his  senses. 

Tlie  Method. — In  giving  an  object  lesson,  the  pupils  should 
first  be  allowed  to  tell  all  they  know  about  the  object.  This 
will  encourage  them  to  prepare  for  the  lesson,  and  add  interest 
to  it,  as  children  love  to  tell  what  they  know.  Second!}',  the 
teacher  should  lead  the  pupils  to  find  out  all  they  can  of  what 
they  have  not  yet  observed  respecting  the  object.  Knowl- 
edge thus  gained  will  be  more  interesting  to  them  than  if 
they  are  told  the  things  by  the  teacher ;  and  will  also  stimu- 
late the  power  of  investigating  for  themselves.  Lastly,  the 
teacher  should  communicate  such  knowledge  as  is  adapted  to 
the  pupil  and  is  appropriate  to  the  subject. 


34  METHODS   OF   TEACHING. 

Telling  their  Knowledge. — The  pupils  should  first  be  allowed 
to  tell  what  they  know.  This  will  give  interest  to  the  study, 
for  children  love  to  talk  as  the  birds  love  to  sing.  It  also 
cultivates  the  habit  of  speaking  from  the  actual  presence  of 
ideas  in  the  mind;  and  of  talking  to  express  thought,  and  not 
to  repeat  words.  This  is  of  supreme  value  in  every  lesson. 
In  this  breaking  away  from  the  repeating  of  words,  and  the 
expressing  of  some  real  idea  in  the  mind,  is  found  the  great 
reform  in  modern  school  education. 

Finding  Out. — The  second  step  in  an  object  lesson  is  to 
lead  the  pupil  to  find  out  knowledge  for  himself.  Here  the 
teacher  begins  the  work  of  instruction;  and  this  is  the  key- 
note of  all  good  teaching.  We  should  smooth  and  brighten 
the  i)athway  of  the  child  all  we  can ;  but  we  must  also  help 
children  to  help  themselves.  We  must  make  them  seekers 
after  truth;  and  not  mere  receivers  of  truth.  To  teach  a 
child  to  long  for  truth  is  better  than  to  give  it  truth;  to 
excite  an  appetite  to  know  is  far  better  than  to  satisfy  this 
appetite.  We  may  thus  make  him  an  original  truth-seeker, 
lay  the  foundations  of  intellectual  power,  and  develop  the 
spirit  which  gives  us  the  world's  philosophers. 

Communicate  Knowledge. — The  last  step  is  that  of  commu- 
nicating knowledge.     In  the  previous  step  the  teacher  was  a 
guide  to  knowledge ;  here   he  becomes  the  source  of  knowl- 
ed'j-e.     All  instruction  should  have  a  teacher  at  its  heart ;  it 
must  contain  the  central  element  of  personality.         This  is 
the  crowning  element  of  the  teacher's  work ;  the  influence  of 
his  own  thought  and  feeling  in  instruction,     A  large-souled 
man  or  woman  projects  his  personality  in  his  instruction  and 
irradiates  what  he  communicates.     He  puts  a  charm  in  knowl- 
edge not  otherwise  seen,  and  inspires  the  hearts  of  his  pupils 
with  a  love  for  learning  not  otherwise  felt.     Only  the  man  or 
woman  who  can  do  this  is  a  teacher  in  the  high  sense  of  the 
*vord,  and  it  needs  the  best  and  rarest  traits  of  character  to 
attain  it. 


LESriOXS    ON    FORM.  85 

JSrrors  to  be  Avoided. — The  teacher  should  be  careful  uot 
to  mistake  the  uature  and  desigu  of  an  object  lesson.  He 
should  remember  that  the  primary  object  is  to  awaken  the 
faculties  of  the  3'oung  mind  into  a  natural  and  healthful  ac- 
tivity ;  and  that  the  secondary  object  is  to  present  a  knowl- 
edge of  the  elementary  facts  of  the  different  sciences.  He 
should  be  careful,  therefore,  to  adapt  his  instruction  to  the 
accomplishment  of  both  these  objects. 

The  teacher  should  be  especially  careful  not  to  teach  words 
without  ideas.  The  thing  to  be  named  should  first  be  clearly 
presented  to  the  mind ;  and  then  the  name  be  given  as  a 
necessity  to  express  the  idea  of  it.  Thus  ever}-  new  word 
becomes  an  expression  of  a  definite  and  clearl}'  defined  con- 
ception. Young  teachers  should  be  especially  careful  to 
guard  against  the  liability  to  teach  names  without  correspond- 
ing ideas. 

Teachers  should  be  careful  also  not  to  give  matter  that  is 
beyond  the  capacity  and  appreciation  of  the  pupil.  Having 
no  text-book  to  guide  them  in  these  lessons,  they  must  rely 
on  their  own  judgment ;  and,  without  experience,  they  will  find 
that  it  is  an  easy  matter  to  get  beyond  the  understanding  and 
appreciation  of  the  pupil.  Great  care  must  be  taken  to  avoid 
this  error,  which  is  a  very  common  one. 

Course  of  Instruction. — A  Course  of  Object  Lessons 
should  embrace  Lessons  on  Form^  Color ^  Parts  of  Objects, 
Qualifies  of  Objects,  Facts  concerning  Objects,  and  the  Ele- 
ments of  several  of  the  sciences,  as  Botany,  Phj'siology,  etc. 

I.  Lessons  ox  Form. 

The  Lessons  on  Form  should  include  all  the  ordinary  geo- 
metrical figures.  These  lessons  ma}-  be  given  with  figures 
made  of  wood  or  pasteboard,  with  diagrams  on  the  board,  with 
geometrical  charts,  etc.  There  are  sets  of  geometrical  figures 
prepared  which  should  be  in  every  school-room.     The  pupils 


86 


METHODS   OF   TEACHING. 


should  I)e  required  to  draw  these  figures  ou  the  slate  and 
blackboard.  This  will  atford  pleasant  employment  for  them 
and  keep  them  out  of  mischief,  as  well  as  give  them  instruction. 
We  present  a  brief  outline  of  the  lessons  on  geometrical 
forms  for  the  aid  of  young  teachers. 


Elements 


PMyijons 


(  Lines, 
j  Angles. 
I  Surfaces. 
I.  Volumes. 

'  Triauerles. 

Quadri  aterals. 

Pentaa:ous. 

He.Kauons. 

Heptagons. 
,  Octagons. 


I  Straiurht. 

I  Curved. 

Lines  ^  Broken. 

Parallel. 

(.Oblique. 


Triangles  < 


f  Square. 

!-D       1,  1   !  Piectansfle. 

Parallelograms  <j  Rhombus. 
1  Rhomboid. 
Trapezoid. 
l_  Trapezium. 

rCube. 
( Prism  I  Parallelopipedon. 
„  ,     ,  I  Triang-ular  Prism,  etc. 

Polyedrons  ^  p.-ramid. 

I.  Frustum  of  Pyramid. 


Round  Bodies 


(  Cylinder. 

rnnp 


Cone 
\  Frustum  of  Cone. 


(.Sphere. 


C  Acute. 
Angles  •<  Obtuse. 

^  f  Equilateral. 
~  I  Isosceles 
cc  (  Scalene. 

^  r  Acute-angled. 
■g -^  Obtuse-anLfled. 
.  J^  (  Right-angled. 

Circumference. 

Diameter. 

Radius. 

Arc. 

Chord. 

Segment. 

Sector. 

Tangent. 

Secant. 

Quaiirant. 

Semi-circle. 

Semi-circumference 


(  Parabola. 
Conic  Sections  -;  Ellipse. 

I  Hyperbola. 

r  C.vcloid. 
Other  Bodies  <  Catenary. 
(  Spirals. 


Circle 


To  the  older  pupils  some  of  the  truths  of  geometry  may  be 
presented,  like  those  found  under  Elementar}-  Geometry,  This 
will  be  the  only  opportunity  the  large  majority  of  pupils  will 
have  to  become  familiar  with  these  truths,  which  will  be  found 
of  real  practical  value  in  life.  ■ 

II.  Lessons  on  Color. 

The  pupil  should  receive  Lessons  on  Color.  He  should  be 
taught  to  distinguish  and  name  all  the  principal  colors.  Such 
lessons  can  be  given  only  by  visible  illustrations,  since  color 


LESSONS   ON    COLOR.  87 

can  be  learned  only  hy  seeing  it.  Every  school  should,  there- 
fore, be  supplied  with  a  "Chart  of  Colors,"  and  a  "Box  of 
Small  Color-cards."  It  will  be  well,  also,  to  have  specimens 
of  worsteds,  pieces  of  silk,  colored  papers,  flowers  in  their 
season,  autumn  leaves,  etc.  There  should  also  be  a  glass 
prism  to  anah'ze  a  sunbeam,  and  colored  crayons  for  the 
blackboard. 

The  teacher  will  first  present  the  principal  colors  on  the 
color  chart,  and  then  pass  around  the  small  cards  or  hold 
them  up  before  the  pupils,  and  have  them  name  the  colors. 
Worsteds,  flowers,  leaves,  and  other  colored  objects,  may  be 
used  in  the  same  way. 

The  teacher  may  also  explain  the  nature  of  color,  that  it  is 
a  modification  of  light,  and  that  all  colors  exist  between  the 
extremes  of  light  and  darkness.  He  may  also  explain  the 
nature  of  light,  that  it  is  the  vibration  of  a  ver^-  rare  fluid 
called  ether,  producing  its  effects  on  the  eye  somewhat  as  the 
vibration  of  air  produces  the  sensation  of  sound  on  the  ear. 

It  will  be  well,  also,  to  call  the  attention  of  the  pupil  to  the 
phenomenon  of  color-blindness.  Many  persons  can  scarcely 
discriminate  between  shades  of  the  same  color;  others  cannot 
distinguish  between  colors  which  are  strikinglj-  opposed  to 
one  another.  There  are  persons  who  can  only  distinguish 
black  and  white,  and  others  who  cannot  tell  red  cherries  from 
green  leaves,  except  by  their  shape.  Amusing  incidents  are 
related  in  illustration  of  this  peculiarity.  An  English  naval 
officer  chose  a  blue  coat  and  red  trousers,  supposing  them  to 
be  of  the  same  color;  and  a  tailor  mended  a  black  silk  vest 
with  a  patch  of  crimson.  Bartholomew,  the  sculptor,  could 
not  distinguish  green  from  red,  and  painted  the  cheeks  of  a 
ladj-'s  portrait  green.  Accidents  have  occurred  on  railroads 
on  account  of  the  engineer  or  flagman  mistaking  colors,  and 
candidates  for  these  positions  are  now  examined  as  to  their 
powers  in  this  respect. 

Calkins,  who  gives  the  above  facts,  also  tells  us  that  out  of 


88  METHODS    OF    TEACHING. 

forty  boys  in  a  school  in  Berlin,  five  could  not  distinguish 
between  common  colors.  "  From  calculations  based  on  exami- 
nations made  in  England  and  Scotland,  it  appeared  that  one 
person  out  of  every  fifteen  was  unable  to  distinguish  all  the 
ordinary  colors;  one  in  fifty-five  confounded  red  with  green; 
one  in  sixty,  brown  with  green ;  one  in  forty-six,  blue  with 
green." 

It  is  not  necessary  to  represent  the  colors  in  this  work,  as 
there  should  be  a  chart  of  colors  in  every  public  school. 
Each  teacher  should  have  a  copy  of  Calkins's  New  Primary 
Object  Lessons,  published  by  the  Harpers,  New  York.  The 
following  facts  and  definitions  will  suggest  to  the  teacher  a 
proper  course  of  instruction  in  color. 

There  are  three  Primary  colors, — Red,  Yellow,  and  Blue.  These  are 
called  primar//  colors,  because  all  other  colors  may  be  formed  from  them. 

The  three  primary  colors,  if  mixed  together,  will  produce  white  light. 
Paint  them  on  a  wheel  in  three  equal  parts,  then  revolve  the  wheel,  and 
it  will  appear  white. 

There  are  seven  Prismatic  colors, — Violet,  Indigo,  Blue,  Green,  Yel- 
low, Orange,  and  Red.  These  are  called  prismatic  colors  because  a  ray 
of  white  light,  passing  through  a  glass  prism,  will  be  divided  into  these 
seven  colors.  The  order  of  these  colors  can  easily  be  retained  by  the 
word  mbgyor. 

Secondary  colors  are  those  which  are  formed  by  mixing  the  primary 
colors.  The  secondary  colors  are.  Orange,  Green,  Indigo,  and  Violet, 
or,  instead  of  the  last  two,  Purple. 

Orange  is  formed  by  mixing  red  and  j'ellow.  Green  is  formed  by 
mixing  blue  and  yellow.     Purple  is  formed  by  mixing  red  and  blue. 

Tlie  ditferent  varieties  of  Bed  are  Maroon,  Crimson,  Scarlet,  Carmine,  Ver- 
milion, and  Piiik.  The  difl'erent  varieties  of  Yellow  are  Citrine,  Lemon, 
Canary,  Straw,  and  Yellow.  The  different  varieties  of  Blue  are  Indigo, 
Ultramarine,  Prussian  Blue,  Light  Blue,  and  Sky  Blue.  The  different  varie- 
ties of  Green  are  Olive  Green,  Emerald,  Pea  Green,  and  Bright  Green.  The 
different  varieties  of  Purple  are  Royal  Purple,  Purple,  Violet,  Lilac,  and  Lav- 
ender. The  ditferent  Varieties  of  Orange  are  Dark  Amber,  Orange,  Salmon, 
Buff,  and  Cream. 

Brown  is  usually  composed  of  red,  yellow,  and  black,  sometimes  modified 
i>y  the  addition  of  white.  The  different  varieties  of  Brown  are  Chocolate, 
Kusset,  Snuff,  Drab,  and  Tan.      Craj/is  composed  of  black  and  white.  wit>  a 


OBJECTS    AND   THEIR   PARTS.  89 

gliglit   mixture  of  red,  j-ellow,  or  black.     The  different  varieties  are,  Slate, 
Pearl   Gray,  Steel  Color,  and  French  Gray. 

Tertiiiry  colors  are  formed  by  mixing  two  secondary  colors,  or  three 
primary  colors  in  the  pniportion  of  two  parts  of  one  and  one  part  of  each 
of  the  other  two  colors.  The  tertiary  colors  are  Citrine,  Olive,  and 
Russet. 

There  are  several  varieties  of  colors,  indicated  by  the  terms  Shade,  Tint,  Hue, 
and  Tinge.  A  Shade  is  formed  by  mixing  black  with  any  color,  so  as  to  make 
it  darker  than  the  oriffinal  color.  A  Ti7U  is  formed  by  mixing  white  with  any 
color,  so  as  to  render  it  lighter  than  the  original  color.  A  Hue  is  formed  by 
combining  two  colors  in  unequal  proportions  ;  as,  a  little  yellow  mixed  with 
pure  red  gives  scarlet,  a  h7ie  of  red.  A  Tirge  is  a  slight  coloring  or  tincture 
added  to  the  principal  color;  thus,  green,  if  it  has  a  slight  coloring  of  yellow, 
is  said  to  have  a  titige  of  3'ellow. 

Two  colors  which,  when  united,  produce  white  light,  are  said  to  be 
Complementary.  Thus,  red  and  green,  orange  and  blue,  yellow  and 
purple,  are  complementary  colors. 

By  the  Harmony  of  Colors,  we  mean  that  relation  of  certain  coiors, 
which  gives  special  pleasure  to  the  eye.  The  complementary  colors  are 
liarmonious.  Since  two  colors  are  harmonious,  which  when  mixed 
together  produce  white  light,  for  harmony  of  color  we  must  have  one 
primary  and  one  secondary  color.  The  teacher  may  show  the  pupil 
that  in  the  scale  of  prismatic  colors,  the  harmonious  colors  stand  to  each 
other  in  the  relation  of  fourths,  like  one  of  the  richest  chords  in  music. 

The  teacher  may  show  the  application  of  the  harmony  of  colors,  bj 
asking  questions  about  ladies'  wearing  apparel,  furnishing  a  room, 
arranging  a  bouquet^  etc. 

III.  Objects  and  Their  Parts. 

Pupils  should  have  lessons  on  Objects  and  their  Parts 
They  should  be  taught  to  know  and  name  the  parts  of  objects. 
For  this  purpose,  teachers  should  have  a  suitable  collection 
of  objects  in  the  school-room.  The  information  concerning 
these  objects,  the  teacher  can  obtain  in  various  ways,  as  here- 
tofore explained.  The  following  outlines,  selected  from  Shel- 
don's Object  Lessons,  will  suggest  a  course  to  the  young 
teacher : 


90 


METHODS    OF    TEACHING. 


1.  Shaft. 

2.  Rins:. 


3.  Barrel. 

4.  Lip. 

5.  Wards. 
.6.  Grooves. 


-•  fl.    Body 


"1 


L  2.    Spire 


'1.  Mouth. 

2.  Lip. 

3    Beak. 
,4.  Canal. 

'  1 .  Whorls. 

2.  Sutures. 

3.  Apex. 


a 


1.  Wood 

2.  Lead. 

3.  Head. 
Poiut. 
Number 

6.  Maker's  Name, 
or  Trade  Mark. 


n.  Blade. 

2.  Bows. 

3.  Limbs. 

4.  Rivets. 

5.  Edj^es. 

6.  Back. 

7.  Point. 

8.  Shaft. 


'1.  Surface. 

2.  Faces. 

3.  Eds:es. 

4.  Milling:. 

.5.  Impression. 
ft.  Imaije. 

7.  Superscription. 

8.  Date. 


1.  Bowl. 

2.  Handle. 

3.  Upper   Rim 

4.  Lower  Rim. 
.5.  Bottom. 

6.  Inside. 

7.  Outside. 

8.  Edges. 


a  (  I.  Head. 

S  -I  2.  Point. 

3.  Shaft. 


(   I    -o    t    f  1-  Front. 
1.  Posts  ]  3   g^^^ 

(1.  Front. 

2 


2.  Rounds  • 


(3. 


1/; 


3.  Back. 

4.  Seat. 

5.  Pillars. 

6.  Spindles. 

7.  Slats. 

8.  Balls. 

9.  Beads. 

10.  Scallops. 

11.  Brace. 


3. 
4. 
5. 
6. 


1.  Upper. 

2.  Sole. 
Heel. 
Tip. 

Eyelets. 
Binding. 

7.  Seams. 

8.  Tongue. 

9.  Lining. 
10.  Insole. 

I  11.  Counter. 
I  12.  Shank. 
1 13.  Welt. 

14.  Strings. 
'  1.5.  Buttons. 
^  10.  Vamps. 


Side. 
Back. 


Ph 


1.  Stem 

2.  Peel. 

3.  Pulp. 

4.  Juice. 
.5.  Veins. 

6.  Dimples. 

7.  Eye. 

8.  Core. 

9.  Seeds. 
10.  Seed-case. 


1.  Bail. 

2.  Handle. 

3.  Ears. 

4.  Body. 

5.  Staves. 

6.  Hoops. 

7.  Bottom. 

8.  Rivets. 

9.  Chime. 
10.  Crole. 


a 


1.  Handle 


2.  Cup 


3.  Tctogue 


1.  Nut. 

2.  Catch. 
.  3.  Shaft. 

4.  Ferule. 

5.  Number. 

1.  Border. 

2.  Rim. 

3.  Edge. 

1.  Loop. 

2.  Clapper. 


a 

o 
o 

< 

C4 


r  1.  Handle 


•a 


r  I.  Shell. 
I  2.  Kernel. 

1.  Nut  -I  3.  Point. 

4.  Scar. 
[5.  Membrane. 
(1.  Scales. 

2.  Cup  \  2.  Edo:es. 

I  3.  Stem. 


1.  Rivets. 

2.  Frame. 

3.  Heel. 

4.  Sides. 

5.  Back. 

6.  Spring. 

7.  Grooves. 

8.  Plate. 


2.  Joint  -I  Pivot. 


3.  Blade    -I 


fl.  Edge. 

2.  Point. 

3.  Back. 

4.  Notch. 
.5.  Sides. 

,6.  Maker's  name. 


QUALITIES    OF    OBJECTS, 


91 


Every  teacher  of  a  primary  or  public  school  should  go  to 
work  and  collect  facts  concerning  other  objects,  and  prepare 
outlines  for  giving  lessons  upon  them.  No  teacher  should  be 
without  a  copy  of  Sheldo7i^s  Object  Lessons,  published  by 
Scribner,  Armstrong  &  Co. 

IV.  Qualities  of  Objects. 

Pupils  should  be  taught  to  distinguish  and  name  the  Quoli- 
ties  of  Objects.  These  qualities  should  be  taught,  not  ab- 
stractly, but  in  connection  with  the  objects  in  which  they  are 
found.  The  pupil  should  be  led  to  perceive  the  quality  in 
the  object,  and  thus  obtain  a  clear  idea  of  it,  and  then  its  name 
may  be  presented  and  fixed  in  the  memory. 

The  following  list  of  qualities  will  suggest  to  the  teacher 
his  work  in  this  respect : 


Hard, 

Brittle, 

Round, 

Woven, 

Soft, 

Flexible, 

Square, 

Cellular, 

Rough, 

Pliable, 

Angular, 

Tubular, 

Smooth, 

Elastic, 

Triangular, 

Netted, 

Stiff, 

Ductile, 

Rectangular, 

Fibrous, 

Limber, 

Malleable, 

Cylindrical, 

Porous, 

Light, 

Buoyant, 

Spherical, 

Twisted, 

Heavy, 

Sonorous, 

Concave, 

Indented, 

Solid, 

Fusible, 

Convex, 

Crystallized, 

Liquid, 

Volatile, 

Spiral, 

Membranous, 

Transparent, 

Natural, 

Saline, 

Translucent, 

Artificial, 

Odorous, 

Opaque, 

Durable, 

Aromatic, 

Brilliant, 

Compressible, 

Edible, 

Adhesive, 

Pulverable, 

Tasteless, 

Tenacious, 

Soluble, 

Pungent, 

Amorphous, 

Insoluble, 

Emollient, 

Inflammable, 

Impervious, 

Sapid, 

Ck)mbustib] 

e. 

Serrated, 

Nutritious. 

V.  Elements  of  Botany. 

Object  lessons  on  the  Elements  of  Botany  may  embrace  the 
flower  and  its  parts,  the  leaf  and  its  parts,  the  names  of 
leaves  from  their /or??is,  the  names  of  leaves  from  their  ma,r- 
gins,  the  names  of  plants,  trees,  etc. 


92 


METHODS    OF   TEACHING. 


The  following  outline  will 

course  in  botany: 

Calyx  -[  Sepals. 
Corolla -{  Petals. 

f  Filament. 

-!  Anther. 


suggest 


Parts 

of 
Flower 


Stamens 

(  Pollen 

r  Style. 
Pistils  <  Stigma. 

(  Ovary. 
Peduncle. 


Parts 

of 
Leaf 


Margins 

of 
Leaves 


Entire. 
Serrate. 
Dentate 
Crenate, 
Repand 
.  Lobed. 


Bases 

of 
Leaves 


'  Cordate. 
Reniforra. 
Auriculate. 
Hastate. 
Sagittate. 


Shape 

of 
Leaves 


Oblique. 

Tapering. 

Clasping. 

Connate. 

Decurrent, 
Orbicular. 
Rotundate. 
Elliptical. 
Oblong. 
Linear. 
Acicular. 
Deltoid. 
Ovate. 
Lanceolate. 
Cordiform. 
Hastate. 
Sagittate. 
Peltate. 
Runcinate. 
Pedate. 


to  the  teacher  a  short 


r  Blade. 
Midrib. 
Vein. 
Veinlets. 
Parenchyma. 
Margin. 
Apex. 
Base. 
Petiole. 
Stipule. 

'  Acute. 
Acuminate. 
Obtuse. 
Truncate. 
-j  RetTise. 
Obcordate. 
Emarginate. 
Mucronate. 
Cuspidate. 


Apices 

of 
Leaves 


Petal 


f  Limb. 
I  Claw. 
Cruciferous. 
Rosaceous. 
Liliaceous. 

f  Banner. 
Corolla  -j  Papilionaceous  ■<  Wings. 

I  Keel. 
Rotate. 
Campanulate. 
Salver-form. 
Funnel-form. 
.  Labiate. 


.  Lyrate. 

In  every  public  school  there  should  be  charts  containing 
diagrams  of  all  these  forms,  and  the  teacher  should  obtain 
specimens  of  them  from  nature.  A  work  recommended  for 
the  teacher  is  Miss  Youmans'si^irs/  Book  in  Botany,  published 
by  Appleton  &  Co. 

There  should  also  be  a  course  of  instruction  on  insects,  birds, 
and  other  animals,  which  may  be  given  by  colored  engravings, 
specimens,  etc. 


LANGUAGE. 


CHAPTER  I. 

THE   NATURE   OF   LANGUAGE. 

LANGUAGE  is  the  instrument  of  thought  and  the  medium 
of  expression.  The  term  is  derived  from  lingua^  the 
tongue,  and  meant  primarily  that  which  came  from  or  was 
moulded  by  the  tongue. 

The  primary  idea  of  language  is  that  it  is  the  means  of 
expressing  our  ideas  and  thoughts.  It  is  the  means  b}'  which 
we  convey  ideas  and  thoughts  from  one  mind  to  another.  It 
is  seen,  moreover,  that  language  is  necessary  to  thought ;  that 
we  think  by  means  of  language.  Sir  William  Hamilton  and 
other  philosophers  hold  that  there  can  be  no  thinking  without 
thought  sj-mbols  ;  that  is,  without  words.  If  we  add  this 
further  use  of  language  to  the  primary  idea  of  expressing 
thought,  we  have  the  definition  given  above. 

Language,  as  it  now  exists,  means  also  the  embodiment  of 
thought  in  words.  It  is  thought  expressed,  as  well  as  the 
power  of  expressing  thought ;  it  is  thought  made  tangible  to 
the  senses  of  sight  and  hearing.  Human  language  has  been 
figuratively  called  the  outward  type  or  forvi  which  thoughts 
and  the  laws  which  regulate  them,  impress  on  the  material  of 
sound.  Plato  sa3"s,  "reason  and  discourse  are  one,"  the 
former  being  the  conA^ersation  of  the  soul  with  herself,  with- 
out the  intervention  of  sound  ;  the  latter  being  this  conversa 
tion  made  audible  by  sound.  Max  Miiller  says, — "  Language 
and  thought  are  inseparable.     Words  without  thoughts  are 

(93) 


94  METHODS   OF   TEACHING 

dead  sounds ;  thoughts  without  words  are  nothing.  To  think 
is  to  speak  low  ;  to  speak  is  to  think  aloud.  The  word  is  the 
thought  incarnate."  Language  is  of  two  kinds  ;  Oral  and 
Written. 

I.  Spokex  Language. 

Definition. — Oral  Language  consists  of  a  combination  of 
articulate  sounds  to  express  ideas.  An  articulate  sound  is 
literally  a  jointed  sound,  and  is  thus  distinguished  from  a 
continuous  sound,  as  a  cry,  etc.  The  sounds  which  are  united 
in  the  formation  of  spoken  words  are  called  elementary 
sounds,  and  consist,  in  our  language,  of  about  forty.  The  ex- 
act number  has  not  been  definitely  determined  by  orthoepists. 

Or  if/in  of  Ltuiguage. — There  are  two  general  theories  for 
the  origin  of  spoken  language, — the  theory  of  Divine  Origin^ 
and  the  theory  of  Human  Origin.  The  theory  of  a  divine 
origin  assumes  that  God  gave  man  a  language  when  he 
created  him,  by  which  he  could  immediately  communicate  his 
ideas  and  thoughts.  In  favor  of  this  theory,  it  is  argued  that 
God  pronounced  His  work  to  be  perfect,  and  tkat  man  would 
not  have  been  perfect  without  the  gift  of  a  language.  It  is 
also  claimed  that  man  must  have  had  a  language,  or  he  could 
not  have  conversed  with  God,  as  he  is  represented  doing  in 
the  Garden  of  Eden. 

The  theor}'  of  a  human  origin  assumes  that  man  had  origin- 
all^'  no  language,  but  merely  the  power  to  form  a  language. 
He  had  the  gift  of  speech  as  he  had  the  gift  of  reason,  and  he 
formed  his  own  language  as  he  has  formed  the  other  arts  and 
sciences.  In  favor  of  this  theory,  it  is  claimed  that  it  is 
natural  to  suppose  an  analog}^  between  the  development  of 
language  and  the  development  of  the  arts  and  sciences.  Man 
was  not  created  with  a  knowledge  of  the  science  of  geometry, 
but  with  powers  by  which  he  could  originate  it.  Language 
was  an  evolution  from  man's  capabilities,  the  same  as  the 
sciences. 


NATURE    OF   LANGUAGE.  95 

It  is  also  claimed  that  the  history  of  languages  shows  a 
growth  and  development  from  rude  beginnings  to  a  more  fin- 
ished form.  It  is  farther  held  that  the  Bible  presents  this 
view,  for  it  says  that  the  animals  were  brought  before  Adam 
to  see  what  he  would  call  them,  "  and  whatever  Adam  called 
them,  that  was  the  name  thereof."  It  is  further  held  that  so 
strong  is  this  power  of  speech  that  children  at  the  present 
time,  if  placed  where  they  never  heard  a  word  spoken,  would 
form  a  language  of  tlieir  own.  Instances  are  recorded  in 
which  the  children  in'a  family  have  actually  formed  a  language 
for  themselves.  It  is  now  the  general  belief  of  writers  upon 
the  subject  that  language  is  of  human,  rather  than  of  divine 
origin. 

Theories  of  Origin. — Assuming  that  language  is  of  human 
origin,  the  question  arises, — How  or  in  what  way  was  it 
formed  ?  Several  theories  have  been  offered  as  the  answer  to 
this  question,  which  have  been  distinguished  as  the  theories 
of  Imitation,  Interjections,  and  Verbal  Roots.  The  first  and 
second  are  also  called  the  Mimetic  and  Exclamatory  theories, 
and  the  last  the  theorj'  of  Phonetic  Types. 

Theory  of  Imitation. — The  theory  of  Imitation  assumes 
that  words  originated  in  the  imitation  of  the  soiinds  of  nature 
Thus  man  heard  a  dog  say  bow-woiv,  and  he  called  it  a  how-woio. 
He  heard  a  sheep  say  baa,  and  he  called  it  a  baa.  He  heard 
a  bee  buzz^  and  he  imitated  the  sound,  and  buzz  became  the 
name  of  a  bee.  It  was  supposed  that  by  this  principle  of 
onomatopoeia  originated  many  such  words  as  crash,  hiss, 
roar,  crack,  thunder,  etc. 

This  theory,  which  was  once  popular,  is  now  generally  dis 
carded  by  philologists.  It  is  probable  that  very  few  words 
originated  in  this  way.  Many  words  which  were  supposed  to 
have  thus  originated,  have  been  traced  to  quite  a  diflerent 
origin.  Thus,  squirrel,  which  was  supposed  to  be  an  imita- 
tion of  the  noise  made  by  the  animal,  has  been  found  to  mean 
a  "shade  tail ;"  cat,  or  the  German  hatze,  which  was  supposed 


96  METHODS   OF   TEACHING. 

to  represent  the  noise  made  by  the  cat,  comes  from  an  expres- 
sion meaning  "an  animal  that  cleans  herself;"  thunder^  which 
was  supposed  to  represent  the  rolling  noise  of  the  clap,  comes 
from  tan,  signifying  to  stretch.  A  few  words,  as  whijjjjoor- 
will,  cuckoo,  etc.,  had  their  origin  in  this  way  ;  but  such  words 
are  sterile,  have  no  reproducing  power,  and  thus  are  not  con- 
sidered to  be  true  words. 

Theory  of  Interjections. — The  theory-  of  Interjections  as- 
sumes that  all  words  originated  from  primar^^  utterances  of 
emotions.  Thus  all  races  emit  certain  similar  ejaculations  to 
express  similar  feelings  of  pain  or  jo3^  The  cry,  the  groan, 
the  laugh,  etc.,  are  common  to  all  mankind.  These  natural 
utterances  are  supposed  to  have  been  the  basis  of  language. 
There  is  no  authority,  however,  for  the  theory,  and  it  has  now 
no  supporters.  Max  Miiller  calls  this  the  Pooh-pooh  theory. 
He  also  calls  the  theory  of  Imitation  the  Bow-wow  theory. 

Theory  of  Verbal  Roots. — The  theory  of  Verbal  Roots 
assumes  that  man  was  primarily  endowed  with  a  "  linguistic 
instinct"  by  which  he  gave  origin  to  verbal  utterances.  These 
primary  utterances  were  very  numerous ;  many  of  them  per- 
ished in  the  struggle  for  life,  but  those  which  remained 
became  the  parents  of  all  the  other  words  of  the  language. 
These  expressions  were  verbal  in  their  character,  and  hence 
are  called  the  verbal  roots  of  the  language ;  and  the  theory  is 
known  as  the  theory  of  Verbal  Roots. 

In  favor  of  this  theory,  it  may  be  argued  that  a  large  part 
of  the  language  can  be  traced  back  to  verbs.  If  we  open  the 
dictionary  for  the  etymology  of  a  word,  we  usually  find  that 
it  is  derived  from  a  verb.  The  preposition  except  was  origi- 
nally the  past  participle  of  the  verb  to  except,  etc.;  and  even 
the  conjunction  if  had  its  origin  in  a  verb  gif,  to  give  or 
grant.  The  importance  of  the  verb,  which  means  the  word 
(verbum),  is  also  a  consideration  in  favor  of  the  theory.  The 
Chinese  call  verbs  living  words,  and  all  others,  dead  ivords. 

The  theory,  however,  is  not  generally  accepted.     Whitney 


NATURE   OF   LANGUAGE.  ^7 

ridicules  it,callino;  it  the  Dirt g-dnng  theory ,a-n  epithet  derived 
from  MuUer's  illustmlioii,  tluit  evervihiuii  .struck  riiiiis,  and 
that  the  mind  of  the  primitive  man.  «Ikmi  stiiu-k  liy  the  (diJL'cts 
of  nature,  rang  out  with  a  sound.  The  theory  was  tirst  pro- 
posed b}-  Heyse,  and  advocated  by  Miiller,  who,  however,  now 
discards  it. 

The  True  Theory. — The  true  theory  for  the  origin  of  lan- 
guage is,  that  it  is  a  natural  outgrowth  of  man's  mental  and 
voeal  powers.  Man  was  gifted  with  the  power  of  thought  and 
feeling,  and  the  faculty  of  exjjression.  He  was  moved  b}-  his 
desires  and  impulses  to  embody-  his  thought  in  vocal  utter- 
ances. These  utterances  were  made  partly  bj'  chance,  aided 
perhaps  by  the  imitation  of  the  sounds  of  nature.  They 
graduall}^  developed  into  more  and  more  perfect  forms, 
through  the  necessity  and  pleasure  of  communication,  and  the 
progress  of  the  race  in  refinement  and  intellectual  culture. 

In  this  evolution,  thought  and  language,  on  account  of  their 
intimate  relation,  must  have  gone  hand  in  hand.  Which  pre- 
ceded the  other,  has  been  a  question  among  philosophers. 
G-eiger  holds  that  man  was  guided  in  his  utterances  b}'  that 
which  he  saw,  and  that  the  use  of  language,  in  a  measure,  pre- 
ceded and  produced  reasoning.  Prof.  Whitney  and  others 
maintain  that  thought  is  anterior  to  language,  and  independ- 
ent of  it ;  and  that  thought  need  not  be  internally  or  externally 
expressed  to  be  thought.  In  fact,  however,  the  two  must  have 
developed  together,  and  langtiage  not  only  expressed  thought 
but  aided  it  in  its  origin  and  growth. 

The  Primitive-  Language. — Which  was  the  primitive  lan- 
guage is  not  positively  known;  the  question,  however,  is  a 
very  old  one.  Herodotus  tells  us  that  Psammitichus,  King 
of  Egypt,  to  ascertain  the  most  ancient  nation,  gave  two  new- 
born children  to  a  shepherd  to  be  brought  up  so  as  never  to 
hear  any  words  spoken.  When  they  were  about  two  years 
old,  they  held  out  their  hands  for  bread  and  cried  "  Becos," 
which  they  continued  to  use  for  the  same  purpose.    This  being 


98  METHODS    OF   TEACHING. 

reported  to  the  king,  he  inquired  what  people  called  bread 
"  Beeos"  ;  and  discovered  that  it  was  the  Phrygians,  and  thus 
inferred  tliat  the  Phrygian  was  the  primitive  language.  James 
IV.  of  Scotland,  in  order  to  ascertain  the  primitive  language, 
placed  a  deaf  and  dumb  woman  with  two  infant  children,  on  the 
solitary  island  of  Inchkeith,  to  see  what  language  they  would 
use  when  they  came  to  the  age  of  speech.  A  Scotch  histo- 
rian, who  gives  the  account,  naively  remarks,  "Some  say  they 
spoke  good  Hebrew;  for  my  part,  I  know  not,  but  from  report." 

Tlic  JJii(//i.s/i  Lfuif/inif/e. — The  historical  origin  and  devel- 
opmiMit  of  the  P^nglisii  language  is  well  known.  The  island 
of  Britain  was  originally  settled  by  the  Celts,  a  branch  of  the 
great  Indo-European  race,  which  had  moved  west,  on  the  wave 
of  emigration,  from  Central  Asia.  Remains  of  the  same  race 
are  found  all  along  the  Atlantic  coasts  of  Europe,  though  they 
were  mainly  congregated  in  Spain,  Gaul,  Britain,  and  the 
adjacent  islands. 

In  the  3^ear  55  B.  C,  the  Romans  under  Julius  Csesar, 
who  liad  previously  conrpiered  Gaul,  passed  over  into  Britain 
and  s^ubdued  and  held  possession  of  it  for  nearly  five  centu- 
ries. Very  few  Latin  words,  however,  were  introduced  into 
the  language  of  Britain  during  the  Roman  occupation,  per- 
hai)s  not  more  than  a  dozen.  A  few  names  of  places  derived 
from  ca,s(ra,  a,  camp,  remain;  as  Chester,  Westchester,  Chi- 
chester, Winchester,  Lancaster,  which  indicate  that  the  mili- 
tary camps  of  the  Romans  became  centres  of  trade,  and  grew 
into  towns. 

About  the  fifth  centurj'  the  northern  barbarians  invaded 
Southern  Europe,  and  threatened  the  overthrow  of  the  corrupt 
and  imbecile  Roman  provinces.  Rome,  to  defend  herself,  was 
obliged  to  withdraw  her  forces,  and  leave  Britain  to  contend 
with  the  tribes  that  surrounded  her.  In  the  j^ear  451  the 
Saxons,  a  Teutonic  tribe  from  the  southern  shores  of  the  Bal- 
tic, undtT  the  lend  of  the  two  brothers,  Hengist  and  Horsa, 
cami'  over  and  settled  on  the  shores  of  tent.     Swarms  of  the 


NATURE   OF   LANGUAGE.  99 

sann!  tribes  followed  from  time  to  time,  and  drove  the  Celts 
into  the  mountains  of  Wales  and  Cornwall.  In  the  year  827, 
about  four  centuries  after  the  invasion,  seven  independent 
kingdoms  had  been  established,  known  as  the  Saxon  Hep- 
tarch3\  The  most  important  of  these  Teutonic  tribes  were 
the  Jutes,  the  Angles,  and  the  Saxons.  The  Angles,  who 
seem  to  have  been  distinguished  for  their  energy  and  intelli- 
gence, though  small  in  numbers,  gave  their  name  to  the  island, 
Eno-land  beinfr  a  modification  of  Angle-land.  The  Saxon  Ian- 
guage  thus  became  the  language  of  the  island,  a  few  Celtic 
names  being  mixed  with  it.  During  the  ninth  and  tenth  cen- 
turies, the  Danes,  a  Scandinavian  tribe,  made  incursions 
and  conquests,  and  introduced  a  few  words  into  the  Saxon 
language. 

In  1066,  "William,  Duke  of  Normandy,  invaded  England, 
and,  by  the  decisive  battle  of  Hastings,  established  himself 
on  the  English  throne.  He  divided  the  island  among  his  fol- 
lowers, and  determined  to  incorporate  the  Saxons  with  the 
Normans,  and  introduce  the  Norman  language  as  the  language 
of  the  island.  To  effect  this,  he  ordered  that  the  youth  in  the 
schools  should  be  instructed  in  the  Norman  language,  that 
the  pupils  of  the  grammar  schools  should  translate  Latin  into 
French,  and  that  all  conversation  in  them  should  be  carried  on 
in  one  of  these  languages.  Pleadings  in  the  courts  were  to 
be  in  French,  deeds  were  to  be  drawn  in  this  language,  no 
other  tongue  was  used  at  court  and  in  fashionable  society. 
So  great  was  this  influence,  that  English  nobles  themselves 
affected  to  excel  in  the  foreign  dialect.  The  mass  of  the  peo- 
ple, however,  at  first  resisted  this  change ;  but  finally,  as  the 
two  peoples  intermingled,  their  languages  intermingled  also, 
and  the  English  language  is  the  result, — the  basis  of  it  being 
Saxon,  and  about  one-third  of  it  being  from  the  Norman 
French. 

The  Norman  French  was  mainly  a  Latin  tongue.  The  Nor- 
mans, or  Northmen,  were  originally  the  inhabitants  of  ancien* 


100  METHODS   OF   TEACHING. 

Scandinavia — Norwa}',  Sweden,  and  Denmark.  Fnder  Rollo, 
about  912  A.  D.,  they  had  conquered  and  settled  in  a  province 
of  France,  where  in  time  they  adopted  the  religion  and  lan- 
guage of  the  French.  The  French  was  a  corrupt  form  of 
Latin,  formed  by  the  mixture  of  the  Latin  introduced  into 
Gaul  by  the  Romans,  and  the  hmguage  of  the  Germanic  tribes 
who  afterwards  conquered  it.  The  Norman  conquest  thus 
introduced  a  large  element  of  Latin  into  the  ?]nglish  lan- 
guage. A  large  number  of  Latin  words  were  subsequently 
introduced  b^'  Latin  scholars  ;  and  in  the  same  way  the  Greek 
element  of  our  language  originated.  Words  of  other  lan- 
guages have  been  introduced  by  business,  commercial  rela- 
tions, etc.  The  English  language  is  thus  a  composite  tongue, 
its  basis  being  the  Anglo-Saxon,  with  about  one-third  Latin, 
a  sprinkling  of  Greek,  and  a  few  words  from  other  tongues. 

Classification  of  Lnnfjnnge. — Attempts  have  been  made 
to  classify  tha  ditferent  languages,  but  no  scheme  has  been 
given  which  is  universal!}-  adopted.  Max  Miiller  speaks  of 
four  distinct  stages  in  the  growth  of  language  :  the  first  being 
the  epoch  of  roots;  the  second  being  the  epoch  of  juxtaposi- 
tion and  concentration,  as  in  the  Chinese ;  the  third  being  the 
agglutinative  stage,  represented  by  the  Turanian  tongues ; 
and  the  fourth  being  the  inflexional  stage,  or  stage  of  amal- 
gamation, represented  by  the  Semitic  and  Ar^^an  languages. 

An  arrangement  based  on  outward  differences  of  form,  that 
will  give  quite  a  clear  idea  of  the  subject,  divides  languages 
into  three  classes  ;  the  Monosyllabic,  the  Agglutinated,  and 
the  Inflected.  The  Monos3'llabic  class  contains  those  lan- 
guages which  consist  only  of  separate  unvaried  monosyllables. 
The  words  do  not  naturallj-  affiliate,  and  the  scientific  forms 
or  principles  of  grammar  are  either  wanting  or  ver}'  imperfect. 
It  includes  the  Chinese  and  Japanese  languages  and  also  the 
dialects  of  the  Xorth  American  Indians.  In  the  Agglutinated 
languages,  the  words  combine  only  in  a  mechanical  way ; 
they  have  no  elective  affinity  and  manifest  no  capabilities  of  a 


>  ■> 


NATURE   OF   LANGUAGE.  lOl 

living  organism.  Prepositions  are  joined  to  nouns  and  pro- 
nouns to  verbs,  but  not  so  as  to  make  a  new  form  of  the 
original  word,  as  in  the  inflected  tongues.  This  class  is  called 
Turanian,  from  Turau,  a  name  of  Central  Asia.  The  principal 
varieties  of  this  family  are  the  Tartar,  Finnish,  Lappish,  Hun- 
garian, and  Caucasian. 

The  Inflected  languages  haA^e  a  complete  interior  organiza- 
tion, with  mutual  relations  and  adaptations.  They  differ  from 
the  Monosyllabic  as  organic  from  inorganic  forms ;  and  from 
the  Agglutinated  as  vegetable  growths  from  mineral  accre- 
tions. This  class  includes  the  culture  of  the  world,  and  in 
their  history  lies  embosomed  the  history  of  civilization. 

To  this  class  belong  two  great  families,  the  Semitic  and  the 
Indo-European.  The  Semitic  embraces  the  languages  native 
to  Southwestern  Asia,  supposed  to  have  been  spoken  by  the 
descendants  of  Shem.  It  includes  the  Hebrew,  Aramiean, 
Arabic,  the  Ancient  Egyptian  or  Coptic,  the  Chaldean,  and 
Phoenician.  The  Semitic  languages  differ  widely  from  the 
Indo-European  in  their  grammar,  vocabulary,  and  idioms. 
On  account  of  the  pictorial  element  in  them,  they  may  be 
called  the  metaphorical  languages,  while  the  Indo-European 
may  be  called  the  philosophical  languages. 

The  two  principal  languages  of  the  Indo-European  stock 
are  the  Aryan  and  the  Graeco-Italic,  or  Pelasgic.  The  word 
Aryan  (Sanskrit,  Arya)  signifies  we.ll-horn,  and  was  applied 
by  the  ancient  Hindoos  to  themselves  in  contra-distinction 
from  the  rest  of  the  world,  whom  they  considered  base-born 
and  contemptible.  The  Pelasgic  comprises  the  Greek  family 
and  its  dialects  and  the  Italic  family-,  the  chief  subdivisions 
of  which  are  the  Etruscan,  the  Latin,  and  the  modern  lan- 
guages derived  from  the  Latin.  The  other  Indo-European 
families  are  the  Lettic,  Slavic,  Gothic,  and  Celtic,  with  their 
various  subdivisions. 

The  Indo-European  languages  are  noted  for  their  variety. 
'  flexibility,  beauty,  and  strength.     They  are  remarkable  for 


102  METHODS   OF  TEACHINQ. 

vitality,  and  possess  the  power  of  regenerating  themselves 
and  bringing  forth  new  linguistic  creations.  They  render 
most  faithfully  the  various  workings  of  the  human  mind — its 
wants,  its  aspirations,  its  passions,  its  imaginings — and  em- 
body and  express  the  highest  products  of  its  thought  and 
philosophy.  Through  them,  modern  civilization,  by  a  chain 
reaching  through  many  thousand  years,  ascends  to  its  primi- 
tive source. 

II.  Written  Language. 

Written  Language  is  the  art  of  expressing  ideas  and 
thoughts  by  means  of  visible  sj-mbols.  It  is  the  embodiment 
of  mental  products  in  a  form  by  which  they  may  be  transmitted 
to  the  mind  through  the  eye,  as  spoken  language  communi- 
cates them  through  the  ear. 

Written  language  may  be  either  ideographic  or  phonetic. 
Ideographic  writing  may  be  either  pictorial,  representing 
objects  by  imitating  their  form,  or  symbolic,  indicating  their 
nature  or  proportions.  Phonetic  writing  may  be  syllabic  or 
alphabetic;  in  the  former  each  character  represents  a  syllable, 
in  the  latter  an  elementary  sound. 

Origin  of  fFritten  Language. — Of  the  origin  of  written 
language,  but  little  is  positively  known.  The  Egyptians 
ascribed  it  to  Thoth,  the  Greeks  to  Hermes  or  Cadmus,  and 
the  Scandinavians  to  Odin.  The  first  step  toward  writing 
was  probably  the  rude  pictorial  representation  of  objects,  the 
next  step  was  the  application  of  a  symbolic  signification  to 
some  of  these  figures.  Pictures,  abbreviated  for  convenience 
and  by  constant  use,  gradually  became  conventional  signs; 
and  at  last  these  characters  became  the  sj^mbols  of  the  sounds 
of  spoken  language. 

Systems  of  Written  Language. — There  have  been  four 
distinct  systems  of  written  language;  the  Ideographic,  the 
Verbal,  the  Syllabic,  and  the  Alphabetic.  These  bear  certain 
historic  relations  to  each  other,  the  last  being  an  outgrowth 


NATURE    OF    LANGUAGE.  103 

of  the  first  through  the  intermediate  stages  of  the  other  two. 
A  brief  description  will  be  given  of  each. 

7'//^  fdeographic. — The  Ideographic  system  (idea,  idea,  and 
grap/io,  1  write),  represented  things  by  pictures  and  symbols. 
Concrete  objects  were  indicated  by  their  pictures,  and  abstract 
ideas  by  their  symbols,  etc.  Thus,  the  sxn  was  indicated  by 
ft  circle  with  a  dot  inside,  0,  the  moon,  by  a  crescent,  with  a 
line  inside,!^  ,  a  mountain  by  three  peaks,  side  b\-  side,  Wf\, 
rani  by  drops  under  an  overarching  line,  /s^  ,  a  child  thus, 
^ .  These  symbols  could  be  combined  to  represent  other 
obje;ts.  Thus  loater  and  eye  combined  represented  tears; 
an  ejr  and  a  dixyr  represented  hearing  ov  understanding. 

Actions  would  be  rL'i)resented  b}-  objects  in  the  attitude  of 
the  act,  Sisfiying  by  a  picture  of  a  flying  bird,  ascending  by 
the  picture  of  a  person  walking  ap  a  hill,  etc.  Some  charac- 
ters were  used  symbolically,  as  a  /< a /k/ to  indicate  a  workman, 
tivo  values  of  a  shell-fish  to  denote  friends.  Relations  could 
also  be  represented,  as  above,  bj'  a  dot  over  a  horizontal  line, 
below  by  a  dot  below  a  horizontal  line,  right  by  the  symbol  1^  , 
and  left  by  "| ,  etc.  These  illustrations  are  taken  from  the 
Chinese  system  of  written  laiii^iiage. 

The  system  of  writing  among  the  Egyptians  was  hiero- 
glyphic, and  is  consi<lered  the  finest  of  the  kind.  The  sun 
with  rays  streaming  from  it,  denoted  light  and  brightness; 
the  moon,  with  its  horns  turned  upward,  denoted  the  viontk. 
They  represented  a  siege  by  a  scaling  ladder,  a  battle  by  two 
hands,  one  holding  a  shield  and  the  other  an  offensive  weapon, 
ingratitude  by  a  viper,  providence  by  an  e^'e,  etc.  Two  legs 
with  the  feet  denoted  movement,  forward  or  backward,  accord- 
ing to  the  direction  of  the  feet,  ^  or  f^.  The  different  emo- 
tions were  indicated  by  the  position  of  a  man  affected  by  them. 
Sometimes  the  symbol  is  purely  metaphorical,  as  when  a  king 
is  represented  by  a  bee,  knowledgehy  a  roll  of  papyrus, /us/zee 
by  the  feather  of  an  ostrich,  because  all  the  feathers  of  that  bird 
were  supposed  to  be  of  equal  length. 


104  METHODS    OF   TEACHING. 

This  kind  of  writing  was  very  early  used  in  Egj'pt  and 
probably  in  most  of  the  ancient  nations.  It  is  the  way  in 
which  rude  races  would  naturall}'  attempt  to  express  their 
ideas  by  characters.  In  Mexico,  when  the  Spaniards  landed, 
intelligence  was  sent  to  Montezuma  by  paintings  on  cloth. 

The  Verbal  System. — The  Verbal  System  is  that  in  which 
the  spoken  words  of  a  language  are  represented  by  a  symbol. 
This  is  but  a  stage  of  the  Ideographic  system.  The  charac- 
ters which  were  at  first  pictures  or  S3-mbols  of  objects^  woiild 
in  time  become  so  modifie<l  that  they  would  no  longer  rep- 
resent the  object,  but  would  be  mere  abstract  symbols  of 
objects  and  ideas.  These  abstract  symbols,  however,  would 
represent,  not  the  spoken  words,  but  the  objects  and  ideas. 
Thus,  in  the  Chinese  written  language,  which  is  largely  verbal, 
each  character  has  a  name  quite  distinct  from  the  name  of  the 
object  represented  by  the  character ;  and  children  are  required 
to  learn  the  character  and  its  name  before  they  learn  what  the 
character  represents.  But  it  is  clear  that  people  would,  in 
time,  besrin  to  make  an  association  between  the  character  and 
the  spoken  word;  and  the  ideographic  system  would  thus 
become,  to  a  great  extent,  verbal. 

The  Syllabic  System. — The  Syllabic  System  is  that  in  which 
the  syllables  of  spoken  words  are  represented  by  characters. 
This  was  a  natural  outgrowth  of  the  ideographic  and  verbal 
systems.  As  soon  as  characters  came  to  be  used  to  represent 
spoken  words,  it  would  be  noticed  that  many  words  consisted 
of  similar  parts,  and  the  idea  would  occur  of  representing 
these  parts  by  means  of  characters.  Thus  all  such  words  as 
eonfer^  contain,  conscience,  etc.,  would  have  a  common  char- 
acter to  represent  the  first  part. 

It  has  been  supposed  that,  at  one  time,  all  the  Asiatic  na- 
tions known  to  the  ancients  under  the  names  of  Syrians  and 
Assyrians  used  the  syllabic  mode  of  writing.  The  Chinese 
language  is  partly  ideographic  or  verbal,  and  partly  syllabic. 
In  it  there  are  2li  elementary  signs  or  keys, -which  are  strictly 


JVATURE    OF    LANGUAGE.  106 

hieroglyphic,  or  abridged  representations  of  visible  objects. 
From  these  214  elements,  all  the  characters  of  the  language 
(80,000,  it  is  said)  are  formed  by  varying  and  com1)ining 
these,  ever}'  compound  character  representing  one  or  more 
syllables  having  a  distinct  meaning. 

The  Alphabetic  System. — The  Syllabic  System  would  lead 
naturally  to  the  Alphabetic  S^'stem.  Having  analyzed  oral 
words  into  syllabic  parts,  the  next  step  would  bo  to  analyze 
syllables  into  their  elements,  and  thus  reach  the  elementary 
sounds  of  the  language,  which  would  be  represented  by  chai*- 
acters.  In  adopting  characters  for  the  elementary  sounds,  it 
would  be  natural  to  select  some  of  those  which  were  already 
in  use  in  the  ideographic  or  sjdlabic  S3-stem,  taking  those 
which  stood  for  words  or  syllables  approximating  the  element- 
ary sounds.  For  example,  the  Egyptian  word,  Ahom,  signi- 
fied an  eagle  ;  the  figure  of  an  eagle,  therefore,  stood,  it  was 
said,  for  the  letter  A,  with  which  the  word  begins.  B  was 
represented  by  a  censer  (Berbe) ;  R  sometimes  by  a  mouth 
(Ro),  sometimes  by  a  tear  (Rime).  An  alphabetic  sj'stem  of 
writing  had  in  this  manner  sprung  up  in  Egypt  (the  hiero- 
gl3'phics  are  partly  alphabetic),  but  it  was  too  imperfect  to 
become  an  instrument  of  popular  literature,  and  some  have 
supposed  that  the  Phcenician  alphabetic  s^'steia  was  formed 
out  of  the  Egyptian  system. 

III.  CoL'RriE  IN  Language. 

Instruction  in  language  includes  ei2;ht  things  :  Learning  to 
Talk,  Learning  to  Read,  Pronunciation,  Orthography,  Read 
ing,   Lexicology,   Grammar,   and    Composition.      There   are 
some  other  divisions,  but  these  are  all  that  are  taught  in  the 
ordinary  public  schools. 

Learning  to  Talk. — The  child  usually  learns   to  talk  at 
home  before  it  is  sent  to  school.     Its  teachers  are  its  parents 
and  the  other  members  of  the  household.     It  learns  by  imi- 
tation and  the  principle  of  association.     It  hears  words  used 
5* 


106  METHODS   OF   TEACHING. 

and  makes  an  association  between  them  and  the  objects  or  ideas 
for  which  they  stand,  and  finally  imitates  them  in  its  attempts  to 
talk. 

This  work  being  done  so  largely  out  of  the  school-room,  does 
not  seem  to  fall  within  the  immediate  province  of  the  teacher. 
Much,  however,  might  be  said  in  advising  parents  to  teach  their 
children  to  talk  correctly  and  with  elegance.  Culture  of  this 
kind  is  of  the  utmost  value  to  the  child.  Habits  of  speech  ac- 
quired in  early  childhood  irom  parents  and  companions,  stick  to 
to  us  through  life  and  are  often  a  blemish  to  high  scholarship. 
Parents  cannot  be  too  careful  in  this  respect.  Aristotle  obtained 
his  elegance  of  language  from  his  mother,  and  Alexander,  it  is 
said,  never  recovered  from  the  bad  habits  acquired  from  Leonides, 
one  of  his  early  teachei-s. 

Teachers  can  also  do  a  great  deal  to  improve  the  oral  language 
of  their  pupils.  Pains  should  be  taken  to  correct  their  mispro- 
nunciations and  grammatical  constructions  so  that  they  may 
speak  correct  and  even  elegant  English  ;  and  they  will  then 
express  themselves  correctly  when  they  come  to  use  written  lan- 
guage. There  should  be  "  talking  classes"  in  the  public  schools 
in  which  the  aim  should  be  to  train  pupils  to  a  ready  and  accurate 
use  of  the  mother  tongue.  Much  of  the  instruction  that  is  now 
given  in  the  reading  classes  could  be  given  in  these  talking 
classes.  Pupils  should  have  exercises  in  "talking  compositions" 
before  they  come  to  "  writing  compositions."  From  these  they 
will  readily  see  that  writing  a  composition  is  merely  "  writing 
their  talk." 

We  urge  teachers  to  take  great  pains  in  moulding  the  oral  lan- 
guage of  their  pupils,  so  that  they  may  become  fluent  and  pleas- 
ing talkers.  The  art  of  conversation  is  one  of  the  most  beautiful 
of  the  arts,  and  we  should  be  careful  that  it  does  not  become 
numbered  among  the  "  Lost  Arts." 


CHAPTER  II. 

»  TEACHING  A  CHILD   TO    READ. 

A  CHILD'S  first  lesson  in  language  is  Learning  to  Talk. 
This  it  receives  in  the  hallowed  precincts  of  home,  where 
the  mother  is  the  teacher.  A  child's  first  lesson  in  language, 
upon  entering  school,  is  Learning  to  Bead.  The  teacher's 
first  work,  therefore,  is  to  teach  the  child  to  read  written  lan- 
guage. In  this  chapter  we  shall  consider  the  methods  of  leading 
a  child  to  a  knowledge  of  written  words. 

The  process  of  Learning  to  Read  consists  in  learning  to  recog- 
nize written  signs,  and  in  associating  spoken  words  with  them. 
It  embraces  two  things;  first,  the  learning  of  sight  symbols,  and 
second,  the  associating  of  sound  symbols  with  them.  The  basis 
of  learning  to  read  is,  therefore,  oral  language. 

From  this  consideration,  several  fundamental  principles  arise 
to  guide  the  teacher  in  the  work.  1.  A  knowledge  of  written 
wonis  should  be  based  on  a  knowledge  of  spoken  words.  2.  There 
shoukl  be  a  transition  from  spoken  to  written  word  signs.  3.  The 
lessons  should  begin  with  words  and  pass  to  sentences  as  in 
spoken  language.  4.  The  first  lessons  should  be  with  words 
relating  to  familiar  objects,  actions,  qualities,  etc.  5.  The 
written  word  should  be  regarded  as  a  representative  of  the 
8i)()keu  word,  as  the  spoken  word  is  the  expression  of  the  object 
or  idea, 

I.  ]\Iethods  op  Teaching. — There  are  several  methods  of 

teaching  a  child  to  read.     The  most  prominent  of  these  are  the 

Al[)habetic  Method,  the  Word  Method,  the  Sentence  Method,  the 

Plionic  Method,  and  the  Phonetic  Method.     All  of  these  have 

been  practiced,  and  nearly  all  of  them  are  still  used,  and  have 

their  advocates, 

(107) 


108  METHODS   OF   TEACHING. 

The  Aljihabetic  3Iefhod.—The  Alphabetic  Method  begins 
by  teaching  the  child  the  names  of  the  letters.  When  these,  or 
a  sufficient  number  of  them,  have  been  learned,  the  child  is 
taught  to  pronounce  words  by  means  of  these  names.  This 
method,  until  within  a  few  years,  was  universally  employed  ;  and 
it  is  still  used  by  a  large  number  of  teachers.  It  is  objec- 
tionable, however,  and  should  be  discarded.  The  objection 
is,  that  the  word  is  not  a  synthesis  of  the  names  of  the  letters, 
neither  do  the  names  suggest  the  i)ronunciation  of  the  word. 
The  subject  will  be  more  fully  discussed  under  pronunciation. 

TJie  Word  Method. — Tlie  Word  Method  begins  by  teach- 
ins:  words  as  wholes,  without  regard  to  the  letters  which  com- 
pose  them.  Among  the  first  to  use  the  Word  Method  was 
Jacotot  (1770-1840),  a  French  philosopher  and  teacher;  the 
most  prominent  advocate  of  it  in  this  country  is  Prof.  Webb, 
and  by  many  it  is  known  as  the  Webb  method.  In  England 
it  is  popularly  known  as  the  "  Look  and  Say"  method,  or  as 
the  method  of  "  Reading  without  Spelling." 

This  is  undoubtedly  a  correct  method  with  which  to  begin 
the  subject.  It  is  really  the  way  in  which  pupils  taught  by 
the  previous  method  actually  learned  to  recognize  words,  for 
when  a  child  spelled  a  word  by  calling  its  letters,  he  knew  no 
more  about  its  pronunciation  than  he  did  before  he  spelled  it. 
The  teacher  gave  him  the  name  of  the  word,  and  when  he  for- 
got it,  named  it  again  and  again,  until  he  made  a  permanent 
association  between  the  sound  s^-mbol  and  the  sight  symbol, 
and  thus  remembered  its  name. 

The  Sentence  Method The    Sentence   Method    is    that 

which  begins  with  sentences  instead  of  letters  or  separate 
words.  By  it  the  child's  attention  is  called  to  some  thought 
orally  expressed,  and  then  the  written  expression  for  this  as  a 
whole  is  presented  and  taught.  The  reason  given  for  this 
method  is  "that  the  sentence  is  the  unit  of  language,"  and 
that  we  read  by  sentences  rather  than  by  words.  It  is  also 
claimed  that  pupils  taught  in  this  "way  read  with  more  ease 


TEACHING   A    CHILD   TO   READ.  109 

and  with  greater  naturalness  of  expression.  It  is  said  that 
in  order  to  read  well,  the  eye  must  be  kept  in  advance  of  the 
voice,  which  this  method  requires. 

There  are  several  objections  to  the  sentence  method.  First, 
it  does  not  begin  at  the  unit  of  language,  which  we  believe  to 
be  the  word  rather  than  the  sentence.  Second,  pupils  taught 
b}^  this  method  very  soon  recognize  the  separate  words,  and 
consequently  read  by  words  rather  than  by  sentence?  Third, 
it  is  impossible  that  all  or  even  a  very  large  number  of  sen- 
tences can  be  taught  in  this  way,  and  eventually  the  child 
must  come  to  the  learning  of  separate  words,  in  order  to  learn 
to  read.  Since  word-reading  must  be  learned  and  used,  it 
seems  best  to  begin  in  this  way. 

The  Phonic  Method, — By  the  Phonic  Method  pupils  are 
taught  to  pronounce  words  by  combining  the  elementary 
sounds  represented  by  the  letters.  It  begins  by  teaching  the 
elementary  sounds  and  the  characters  which  represent  them. 
It  uses  the  twenty-six  characters  of  the  alphabet  to  represent 
twenty-six  sounds,  and  then  employs  a  notation  to  indicate 
the  remaining  sounds.  It  also  indicates  the  silent  letters  of 
words  by  printing  them  in  italics  or  a  different-faced  type. 

The  Phonic  Method  is,  beyond  question,  the  correct 
method  of  teaching  pupils  to  pronounce  words.  It  is  natural 
and  simple,  and  enables  a  pupil  to  pronounce  a  new  word  in- 
dependently of  the  teacher.  In  connection  with  the  Word 
Method,  it  is  the  true  method  of  teaching  a  child  to  read.  It 
will  be  discussed  more  in  detail  under  Pronunciation. 

The  Phonetic  MetJmd. — The  Phonetic  Method  is  in  princi- 
ple similar  to  the  Phonic  Method.  It  begins  by  teaching  the 
elementary  sounds  and  the  characters  which  represent  them. 
It  uses  the  twenty-six  letters  of  the  alphabet  to  represent 
twenty-six  sounds,  and  then  invents  other  characters  to  rep- 
resent the  remaining  sounds,  it  spells  the  words  as  they  are 
pronounced,  using  only  as  many  characters  as  are  sounded, 
and  requires  the  pupil  to  make  a  transition  from  the  phonetic 


110  METHODS    OF   TEACHING. 

form  of  the  -word  to  the  ordinary  form.     It  will  be  further 
considered  under  Pronunciation. 

II.  The  True  Method. — Havins;  stated  the  several  methods 
by  which  a  child  may  be  taught  to  read,  we  proceed  to  describe 
what  we  regard  as  the  correct  method  in  practice.  The  true 
method  consists  of  a  combination  of  the  Word  Method  and 
the  Phonic  Metliod.  We  should  bcsfin  with  the  Word  Method, 
and  after  the  child  becomes  familiar  with  a  number  of  words, 
and  can  read  little  sentences,  we  should  analyze  the  words 
into  their  elementary  sounds  and  characters,  and  thus  connect 
with  it  the  Phonic  Method. 

The  Word  Method. — The  True  Method  begins  with  words. 
The  proper  place  for  a  child  to  begin  to  leani  to  read  is  not 
with  the  letters  of  a  word,  but  with  the  word  itself.  The  rea- 
sons for  this  are  many,  a  few  of  which  will  be  stated. 

First,  the  Word  is  the  Unit  of  language.  Language  begins 
with  words,  not  with  letters  or  sentences.  Letters  are  the 
fractions  of  written  words,  and  we  should  not  begin  with  frac 
tions.  Sentences  are  the  syntheses  of  linguistic  units,  and  the 
units  should  precede  their  combination.  Second,  it  coincides 
with  the  manner  of  learning  oral  language.  The  child  begins 
language  with  spoken  words,  and  not  with  their  elements, 
the  eleraentar}'  sounds.  It  would  be  as  sensible  for  a  mother 
to  teach  her  child  to  talk  b^'  beginning  with  the  elementary 
sounds,  as  for  one  to  teach  a  child  to  read  by  beginning  with 
the  letters.  • 

Third,  it  is  in  accordance  with  a  fundamental  principle  of 
teaching, /rom  the  known  to  the  unknown.  We  begin  with  the 
spoken  word  which  is  known,  and  pass  from  it  to  the  unknown 
written  word.  To  begin  with  the  letters,  is  to  deal  entirely 
with  the  unknown,  as  these  abstract  and  arbitrary -sj'mbols 
cannot,  except  in  a  few  instances,  be  associated  with  anything 
known.  Besides,  the  method  of  beginning  with  words  is 
much  more  interesting  to  the  child,  as  in  a  few  lessons  he  is 
reading  little  sentences  which  he  understands. 


J 


TEACHING    A    CHILD   TO    READ.  Ill 

Fourth,  to  begin  at  the  word  as  a  Avhole,  and  pass  to  its 
parts,  proceeds  hy  analysis,  which  is  the  natural  way  in  which 
a  little  child  acquires  knowledge.  It  knows  a  horse  or  a  tree, 
not  by  beginning  with  their  parts  and  uniting  them  into  one 
complete  object,  but  by  first  knowing  them  as  wholes,  and 
subsequently  becoming  familiar  with  their  parts.  The  natu- 
ral law  of  instruction  is  from  the  whole  to  the  parts;  first 
analj'sis  and  then  synthesis. 

For  one  who  has  not  used  this  method,  it  is  natural  to  think 
that  a  child  cannot  know  a  written  word  without  knowing  the 
letters  which  compose  it.  This,  however,  is  a  mistake.  We 
do  not  anal3'ze  a  word  into  its  letters  when  we  read,  any  more 
than  we  analj^ze  an  object,  like  a  horse,  into  its  parts,  in  order 
to  be  able  to  know  what  it  is.  We  know  the  object  as  a  whole, 
at  a  glance,  and  remember  its  name;  so  we  know  a  word  by 
its  general  appearance,  just  as  we  know  a  picture  or  an  object. 
It  stands  before  the  mind  as  a  picture  of  an  idea  or  of  a 
spoken  word. 

It  may  also  be  objected  that  all  words  cannot  be  learned  in 
this  way;  and  that  the  pupil  acquires  no  power  to  pronounce 
independently  of  the  teacher.  The  same  objection  applies  to 
the  alphabetic  method,  from  whose  advocates  this  objection 
is  liable  to  come.  The  fact  is,  that  both  should  be  followed 
by  the  phonic  method,  by  which  a  pupil  may  learn  to  pro- 
nounce independentl}'^  of  the  teacher. 

The  method,  however,  becomes  more  than  a  "  look  and  sav" 

7  7  */ 

method  to  the  learner.  The  child  soon  begins  to  make  com- 
parisons, and  discover  analogies  which  aid  him  in  pronuncia- 
tion. The  teacher  may  advert  to  no  principle  of  sound,  but 
the  child  does  so  spontaneously'  and  unconsciousl3^  The  as- 
sociation of  sound  with  sign  which  he  makes  in  one  word,  he 
endeavors  to  apply  in  other  analogous  words,  as  any  one  will 
notice  who  observes  carefull}-.  He  thus  learns  to  pronounce 
many  words  independently  of  the  teacher,  as  he  does  ni 
using  the  alphabetic  method. 


112  METHODS   OF   TEACHING. 

Tlie  First  Step,  therefore,  in  teaching  a  chikl  to  read,  is  to 
begin  with  the  written  word,  as  the  child  begins  spoken  lan- 
guage with  the  spoken  word.  The  first  lesson  is  a  lesson  on 
printed  words.  We  should  begin  with  some  familiar  spoken 
word  which  the  child  knows,  and  then  pass  to  the  written 
word,  and  make  it  known.  We  teach  a  few  woi'ds  in  this  way 
and  then  unite  them  into  sentences,  and  have  the  child  read 
little  sentences.  After  he  has  been  reading  several  days,  or 
a  few  weeks,  if  the  teacher  prefers,  we  should  pass  to  the 
Phonic  Method. 

Phonic  Method. — The  Second  Step  is  to  pass  to  the  elements 
of  words.  As  there  are  two  classes  of  words,  oral  and  written, 
so  there  are  two  classes  of  elements  of  words.  The  elements 
of  spoken  words  are  the  eZemen^ar?/ souncZs;  the  elements  of 
written  words  are  the  letters. 

It  has  been  a  question  which  elements  we  should  present 
first,  the  sounds  or  the  letters;  but  it  is  a  question  easily 
answered.  Since  we  learn  spoken  words  before  written  words, 
we  should  first  analyze  the  spoken  words  into  their  elements, 
and  subsequently  teach  the  characters  which  represent  them. 
By  analyzing  a  word,  as  cat,  we  show  the  pupil  that  a  spoken 
word  consists  of  distinct  sounds ;  we  then  teach  him  to  make 
these  sounds,  and  afterward  teach  the  characters  which  rep- 
resent them.  In  this  way  the  letters  are  introduced  as  S3'm- 
bols  of  sounds,  and  not  as  abstract  characters  with  names. 

In  presenting  these  characters,  since  some  letters  represent 
different  sounds,  it  is  necessary  to  introduce  a  system  of  no- 
tation to  indicate  the  sound  of  those  characters  that  represent 
moi-e  than  one  sound.  This  notation  may  be  the  figures  1,  2, 
3,  etc.,  used  as  indices  or  subscripts,  or  the  notation  of  the 
dictionary'.  In  practice,  it  will  be  best  to  use  the  notation  of 
the  reader  or  speller  used  in  the  school. 

It  is  also  necessary  to  indicate  the  silent  letters  of  Avords, 
so  that  pupils  may  know  just  what  letters  are  to  be  sounded 
in  pronouncing  printed  words.     This  can  be  done  by  printing 


TEACHING  A  CHILD  TO  READ.  113 

such  letters  in  italics,  as  is  the  general  custom,  or  in  a  lighter 
faced  type,  as  in  Dr.  Leigh's  method,  or  by  printing  them  with 
a  stroke  across  them,  as  is  done  in  Appleton's  series  of 
readers. 

The  Third  Step  is  to  require  the  pupil  to  pronounce  words 
by  combining  the  sounds  of  the  letters  which  they  see  com- 
bined in  the  words.  Thus,  when  he  sees  the  word  hat,  he 
knows  the  first  sound  is  that  of  6,  the  second  ah,  and  the  third 
the  aspirate  t;  and  uttering  these  sounds  in  their  order,  he  has 
the  correct  pronunciation  of  the  word  bat.  Or,  suppose  the 
word  is  ^ght;  he  sees  that  g  and  A  are  not  to  be  sounded,  and 
he  gives  the  sounds  of  /,  z,  and  t,  one  after  another,  so  that 
they  coalesce,  and  he  has  the  correct  pronunciation  of  the 
word  fight.  The  pupil,  becoming  familiar  with  the  words 
printed  in  this  form,  will  readily  recognize  them,  and  be  able 
to  pronounce  them  when  printed  in  the  ordinary  form. 

Last  of  all,  teach  the  names  of  the  letters  and  their  order  in 
the  alphabet.  Should  it  be  asked  how  soon  the  names  of  the 
letters  should  be  introduced,  we  answer  that  if  the  pupils 
know  the  names  of  the  letters  by  the  time  thej^  have  com- 
pleted the  primer  or  primary  reader,  it  is  sufficient  for  all 
practical  purposes.  They  have  ver}-  little  use  for  their  names, 
and  may  distinguish  them  by  their  sounds  at  first. 

Model  Lesson. — To  illustrate,  suppose  we  begin  with  a 
common  word  like  cat.  I  ask  some  questions  and  talk  about 
a  cat.  I  then  point  to  the  picture  of  a  cat  on  the  card  or  in 
the  book,  and  ask  its  name,  which  the  pupils  give  me.  I  then 
call  attention  to  the  fact  that  all  these  sounds  which  we  make 
when  we  talk  are  called  words.  I  then  lead  them  to  notice 
that  the  words  which  the}'  know  are  those  which  they  hear. 
I  then  tell  them  that  there  are  also  words  which  the}'  can  see, 
and  awaken  an  interest  to  know  such  words.  I  then  point 
out  the  word  cat  on  the  card  or  in  the  book,  and  tell  them 
that  it  is  the  visible  or  written  word  cat.  In  the  same  way  I 
teach  the  written  words  that  represent  other  objects. 


114  METHODS    OF   TEACHESTG. 

I  next  teach  written  words  that  are  not  the  names  of 
objects.  I  have  the  pupils  say  something  about  an  object ;  as, 
"I  see  a  cat,"  and  then  show  them  this  sentence  on  the  card 
or  in  the  book,  or  I  write  it  on  the  board ;  and  then  teacli 
them  each  word  of  this  sentence.  I  do  the  same  with  other 
sentences,  making  use  of  some  of  the  words  already  learned, 
and  proceed  thus  as  far  as  I  deem  it  advisable.  In  this  way 
I  pass  from  audible  speech  to  visible  speech. 

After  the  pupils  have  learned  quite  a  number  of  words  and 
read  several  pages  in  their  primer,  I  proceed  to  the  analysis 
of  words  into  their  elements.  To  give  them  an  idea  of  tlie 
elements  of  words,  I  first  take  some  object,  as  a  knife^  and 
lead  them  to  see  that  it  consists  of  parts.  I  then  take  some 
oral  word,  as  cat,  and  pronouncing  it  slowlj- ,  separate  it  into 
its  three  phonetic  elements,  the  sounds  of  c,  a,  and  t^  and  let 
them  hear  that  this  word  consists  of  three  distinct  sounds.  I 
then  have  the  pupils  give  these  elements,  imitating  the  sounds 
as  I  make  tliem.  I  then  teach  them  the  letters  (not  their 
names)  c,  a,  and  t,  which  represent  these  sounds.  I  then 
have  them  unite  these  sounds  in  succession,  as  they  see  the 
letters  united  in  the  word,  and  thus  pronounce  the  word.  I 
pi'oceed  in  the  same  way  with  other  words  and  sounds  until 
the  pupils  can  pronounce  words  quite  readil3^ 

As  the  different  sounds  of  the  same  letter  are  presented,  we 
must  introduce  a  notation  to  indicate  the  sound  of  the  char- 
acter, and  also  show  how  the  silent  letters  are  represented. 
Use  at  first,  also,  onl}-  words  of  simple  and  regular  formation, 
omitting  such  words  as  tongue,  thought,  knife,  etc. 

General  Suggestions. — We  should  teach  the  short  sounds 
of  the  vowels  first,  as  a  in  ai,  e  in  en,  i  in  in,  o  in  on,  u  in  us; 
and  the  simple  consonants,  as  b,  rf,  /,  I,  m,  n,  p,  etc.  We 
should  then  drill  the  pupil  in  pronouncing  their  combinations 
.n  words  of  two  letters,  as  an,  at,  in,  ox, etc.  Then  words 
of  turee  letters  ma}'  be  given,  as  fan,  bat,  bit,  box,  fox,  etc. 
We  should  then  introduce  some  of  the  other  sounds  of  the 


I 


TEACHING    A    CHILD   TO    READ. 


115 


vowels,  as  a,  e,  i,  o,  etc.,  indicating  them  bj-  the  proper  nota- 
tion, and  combine  these  with  the  characters  already*  given. 
Next  show  how  silent  letters  are  represented,  and  introduce 
such  words  as  can(^,  rate,  fate,  mate,  fine,  line,  etc. 

The  teacher  may  use  the  blackboard  in  teaching  pronuncia- 
tion with  great  advantage.  Let  him  write  the  letter  a  on  the 
board,  and  have  the  pupils  give  its  sound  ;  then  place  the 
letter  t  after  it,  and  have  the  pupils  give  its  sound,  and  also 
the  sound  of  the  combination  at;  then  place  the  letter  bat  the 
left,  have  the  pupils  give  its  sound  and  the  sound  of  the  com- 
bination bat.  Then  erase  the  b  and  substitute  each  of  the 
consonants  /,  r,  ??i,  n,  s,  and  v  in  its  place,  and  require  the 
pupils  to  pronounce  the  woi'd.  A  similar  exercise  may  be 
had  on  other  combinations. 

To  aid  the  pupils  in  learning  new  words,  columns  of  similai 
words  may  be  written  on  the  board  so  that  the  pupils  may  see 
their  pronunciation  parti}'  b}'  the  analogy  of  words.     Thus: 

cat  in  car  ten  bit 

rat  tin  far  hen  fit 


hat 
fat 


in 
tin 
pin 
fin 


car 
far 
tar 
mar 


gun 
fun 


pen 
fen 


pit 
sit 


run 

sun. 


They  may  also  be  arranged  so  that  the  common  element 
may  be  seen  and  readih'  joined  with  the  different  single  ele- 
ments. Thus,  take  the  combinations  at,  an,  ot,  og,  and  ill, 
which  we  suppose  the  pupils  have  learned,  and  combine  them 
with  the  different  consonants,  as  is  indicated  below. 


at- 


b-at 

c-an 

c-at 

f-an 

f-at 

an  \  m-an 

h-at 

p-an 

r-at 

r-an 

02 


b-og 
c-og 
d-og 
f-og 
l-osj 


Classes  of  words  may  also  be  selected  which  have  the  com 
mon  element  first,  as,  cat,  can,  cap,  cab,  etc.      These   words 
could  be  grouped  in  books  or  on  cards,  or  may  be  written  on 
the  blackboard.     The  method  of  using  such  exercises  is  so 
evident  that  we  need  not  describe  it.     It  is  remarkable  how 


116  METHODS   OF  TEACHING. 

soon  children  acquire  the  sounds  of  letters,  both  consonants 
and  vowels,  and  when  this  is  done,  they  have  the  key  to 
reading  in  their  hands. 

It  would  be  well  to  have  words  arranged  in  columns  in  the 
reader  or  spelling-book,  classed  according  to  their  analogies  of 
sound,  with  the  character  or  combination  of  characters  used 
to  represent  the  sound  placed  at  the  head  of  the  lesson  to 
serve  as  a  key  to  the  pronunciation.  Thus  a,  as  in  late,  would 
indicate  the  sound  of  such  words  as  aim,  they,  nail,  steak^ 
gauge,  etc.;  or  sh  in  ship  would  be  the  key  to  the  pronuncia- 
tion of  words  which  contain  the  combinations  ti,  si,  ci,  ch,  ce, 
se,  sch,  etc. 

The  pupil  should  also  have  plenty  of  exercise  in  forming  new 
words  by  combining  the  sounds  of  the  characters  as  already 
explained.  The  small  letters  are,  of  course,  to  be  taught  first. 
The  pupils  should  be  required  to  write  the  letters  and  the 
words  on  their  slates  and  on  the  blackboard. 

After  the  pupils  have  learned  to  read  by  the  word  method 
and  the  phonic  method,  I  should  have  them  name  the  letters 
of  words,  and  pronounce  the  words.  This  was  the  old  method, 
and  pupils  will  find  it  convenient  to  be  able  to  name  the  letters 
of  words,  though  the  names  of  the  letters  will  not  enable  them 
to  pronounce  the  word. 

It  will  thus  be  seen  that  the  true  order  of  teaching  a  child 
to  read  is, — Jirst,  the  object  or  idea  ;  second,  its  sound  symbol, 
or  spoken  word;  third,  the  form  symbol,  or  printed  word; 
fourth,  the  elements  of  the  spoken  word,  or  the  elementary 
sounds;  fifth,  the  elements  of  written  words,  or  the  letters 
representing  the  elementary  sounds ;  and,  sixth,  the  synthesis 
of  these  sounds,  as  the  pupil  sees  the  letters  united  in  the 
printed  words.  Subsequently,  the  pupil  may  be  taught  to 
represent  the  words  by  writing  them  on  the  slate  or  black- 
board. This  is  the  true,  simple,  and  natural  method ;  and  this 
order  of  learning  to  read  the  language  will  correspond  with 
the  order  of  using  it.     Words,  then,  will  become  as  mirrors 


TEACHING   A   CHILD  TO   READ.  »  117 

reflecting  objects  and  ideas  to  the  minds  of  pupils.  Sense  and 
sound,  and  form  and  use,  will  become  so  intimately  blended 
together  that  pupils  may  easily  be  led  to  use  conversational 
tones  in  reading,  and  a  natural  style  of  expression  will  follow 
as  a  natural  result. 

In  this  work  of  instruction,  the  teacher  may  use  Books,  or 
Beading  Cards,  or  the  Blackboard.  Each  one  of  these  has 
its  own  peculiar  advantages  ;  and  in  actual  instruction  it  will 
be  best  to  combine  the  use  of  them  all.  Every  primary  school 
should  be  supplied  with  a  set  of  Reading  Cards,  and  the 
•teacher  should  practice  until  he  can  write  the  words  neatly  on 
the  board.  The  pupils  should  also  be  taught  to  write  words  on 
the  slate  and  blackboard.  The  use  of  script  letters  is  proposed 
as  they  are  more  easily  read  ;  and  pupils  have  no  difficulty  in 
making  the  transition  from  the  script  forms  to  the  printed  forms. 
Some  teachers  may  prefer  to  have  their  pupils  print  the  words 
on  the  board  rather  than  to  write  them  in  script  letters ;  but  this 
will  not  change  the  character  of  the  method  we  have  suggested. 


CHAPTER  III. 

TEACHING  THE   ALPHABET. 

IN  teaching  a  child  to  read,  we  have  used  the  letters  as  rep- 
resenting sounds,  though  we  have  not  called  atte;ition  to 
their  form  or  their  names.  The  next  step  is  to  make  a  child 
fam'liar  with  the  forms  and  names  of  the  letters.  Since  some 
knowledge  of  the  origin  and  nature  of  the  alphabet  will  be 
interesting  to  teachers,  we  shall  divide  this  chapter  into  two 
parts;  the  Nature'of  the  Alphabet  and  the  Methods  of  Teach- 
ing the  Alphabet. 

I.   The  Nature  of  the  Alphabet. 

Definition. — The  Alphabet  is  a  system  of  characters  used 
to  represent  the  elementary  sounds  of  a  language.  The  term 
alphabet  is  derived  from  alpha  and  beta,  the  first  two  letters 
of  the  Greek  alphabet.  It  comes  to  us  from  the  Latin  alpha- 
betum,  which,  however,  it  is  said,  occurs  in  no  prose  writer 
before  Tertullian,  though  it  is  presumed  that  the  word  had 
previously  existed. 

Origin. — Our  alphabet  was  derived  from  the  Latin,  which 
was  derived  from  the  Greek,  which,  it  is  supposed,  was  derived 
from  the  Phoenician,  or  from  the  Hebrew,  with  which  it  is 
closely  allied.  It  is  said  that  Cadmus,  1500  B.  C,  brought 
16  letters  into  Greece;  Palamedes  subsequently  added  4,  and 
Simonides  4  more,  which  accounts  for  the  24  letters  of  the 
Greek  alphabet. 

The  forms  of  our  alphabetic  characters  are  derived  from  the 
Phoenician  letters.  The  origin  of  these  primitive  forms  is  not 
positively  known.     It  has  been  supposed,  but  without  author- 

(118) 


NATURE  OF  THE  ALPHABET.  119 

ity,  that  they  originally  represented  the  shape  of  the  mouth  in 
making  the  sound.  It  is  now  generally  believed  by  those  who 
have  investigated  the  subject,  that  they  are  modifications  of 
the  system  of  hieroglyphics,  or  picture-writing,  used  in  Egypt. 
The  Phoenicians  probably-  took  the  Egyptian  characters,  which 
were  symbols  of  words,  and  changed  them  into  symbols  of 
sounds. 

Greek  Cluntges. — In  adopting  the  Phoenician  alphabet,  the 
Greeks  made  manj'  considerable  changes  in  the  values  of  the 
sj'mbols.  Several  of  them  were  unnecessary,  for  they  had  no 
sounds  in  their  language  to  correspond  with  them,  and  they 
were  dropped.  The  Phoenicians  had  no  proper  vowels  ;  the 
Greeks  therefore  emplo^-ed  as  such  those  letters  which  were 
nearest  akin  to  vowels;  A,  E,  F,  H,  I,  and  0.  To  the  Phoeni- 
cian alphabet  the  Greeks  added  the  aspirates  *  and  x,  the 
double  consonant  4',  and  the  sign  for  long  o,  a,  placing  these 
new  letters  at  the  end.  To  distinguish  these,  the  short  o  was 
called  "0  uiKo&v,  small  o;  and  the  long  o^'Qfj.iya,  great  o.  A  few 
other  changes  were  made,  which  we  cannot  here  notice.  The 
Greek  alphabet,  in  its  complete  form,  was  first  adopted  by  the 
lonians.  It  was  first  used  in  Attic  inscriptions  in  the  archon- 
ship  of  Euclides,  403  B.  C. 

Latin  Changes, — The  Latins  also  introduced  many  changes, 
as  (1)  in  the  use  of  the  symbol  (F)  uaw,  to  denote  not  the 
V  but  the  /  sound,  which  was  probably  strange  to  the  Greeks; 
(2 )  in  allowing  K  to  fall  almost  out  of  use,  and  emploj'ing  C 
instead;  (3)  in  forming  a  new  symbol  G,i.  e.,  C  with  a  distin- 
guishing line,  to  mark  the  soft  gutturals,  about  the  3d  cen- 
tury B.C.;  (4)  in  the  addition,  in  the  1st  century  B.  C,  of  the 
two  symbols  Y  and  Z  after  X  (which  had  long  been  the  last 
letter  of  the  alphabet),  to  express  the  Greek  sounds  v  (upsilon) 
and  2  (zeta). 

English  Clianges. — The  alphabet,  as  derived  from  the 
Latin,  has  been  somewhat  modified  in  the  English  language 
Thus  I  and  J,  which  were  at  first  merely  graphic  variations. 


120  METHODS   OF   TEACHING. 

were  changed  by  the  Dutch  printers  during  the  16th  and  17th 
centuries,  to  represent  ditfereut  sounds.  The  letters  U  and  V, 
which  were  formerly  used  indiscriminately  to  represent  the 
same  sound,  acquired  separate  uses  about  the  same  time.  W 
was  added  some  time  during  the  Middle  Ages.  It  is  a  com- 
bination of  two  Vs,  the  letter  v  being  formerly  called  m,  which 
accounts  for  the  name  "  double  u." 

Order  of  Characters. — When,  by  whom,  and  why  the  let- 
ters of  the  alphabet  were  arranged  as  we  now  have  them, 
cannot  be  explained.  The  present  arrangement  has  given  rise 
to  much  ingenious  speculation.  It  has  been  supposed  by 
some  that  there  are  traces  of  regularity  in  the  present  order. 
Thus,  the  three  soft  momentary  sounds  6,  gr,  d  were  placed 
together;  p,  k,  and  t  may  have  once  been  together  and  sepa- 
rated by  later  intrusions ;  /,  m,  and  n  have  an  affinity  indi- 
cated b\'  the  name  liquids,  etc.  It  is  hardly  probable,  how- 
ever, that  the  symbols  were  arranged  upon  any  scientific 
method;  but  that  chance  guided  the  general  arrangement, 
though  a  few  sounds  obviously  similar  may  have  been  put 
together  intentionally. 

Karnes  of  Letters. — The  Romans  also  changed  the  Greek 
names  for  the  characters  of  the  alphabet.  The  vowels  were 
known  by  their  sounds  only.  The  momentar}-^  consonants  and 
h  were  denoted  by  their  own  sound  followed  by  a  vowel ;  as, 
be,  ce,  de,  ge,  pe,  and  te,  and  also  ka  and  ha;  q  had  sufficient 
vowel  sound  to  float  it  alone  ;  on  the  other  hand,  the  continu- 
ous consonants  were  preceded  by  a  vowel;  as,  ef,  el,  em,  er, 
es ;  and  x  was  called  ix. 

This  difference  in  the  method  of  naming  the  consonants  was 
obviously  caused  by  their  nature.  Momentary  sounds  are  pro- 
duced by  a  complete  closure  and  opening  of  the  organs  re- 
quired in  each  case  ;  when  this  opening  is  made,  the  organs 
are  so  placed  as  to  form  a  vowel,  which  is" naturally  produced 
by  the  remnant  of  sound  required  for  the  consonant ;  whereas 
a  vowel  cannot  be  produced  before  any  one  of  these  sounds 


NATURE    OP   THE   ALPHABET.  121 

without  conscious  effort ;  hence  it  is  simpler  to  call  ^,^(7,  than 
to  call  it  ak.  The  continuous  sounds,  however,  are  produced 
with  the  organs  slightly  oj)en,  in  which  case  a  certain  aniouiil 
of  vowel  sound  tends  to  escape  just  as  the  organs  are  drawing 
together  to  produce  the  consonant,  and  is  thus  heard  before 
it;  but  to  sound  a  vowel  after  one  of  these  consonants,  the 
organs  must  intentionally  be  put  in  the  proper  position. 
Thus,  the  same  principle — the  conscious  or  unconscious  striv- 
ing for  ease  of  articulation — produces  opposite  results  in  the 
case  of  the  momentary  and  continuous  consonants. 

The  same  principle  caused  a  different  vowel  to  be  used  for 
h  and  ^,  from  that  which  is  used  for  the  other  letters.  In 
sounding  the  letter  a  (ah),  the  organs  are  in  nearly  the  same 
position  as  in  sounding  these  two  gutturals,  only  a  little  more 
open  ;  whereas  the  position  for  sounding  e  (ay)  is  more  nearly 
that  of  all  the  other  consonants.  The  sound  of  e,  as  here  used 
is  ay,  and  of  a,  is  a/i,  which,  it  is  supposed,  was  the  Latin  sound, 
thus  a  Roman  would  have  spoken  of  learning  not  his  a-bee-see, 
but  his  ah-bay-kai) . 

Classi/icafioit. — The  letters  of  the  alphabet  have  been  clas- 
sified with  respect  to  their  history*,  as  follows:  (1)  B,  D,  H, 
K,  L,  M,  N,  P,  Q,  R,  S,  and  T,  letters  from  the  Phuiuicians ; 
^'2)  A,  E,  I,  0,  Z,  originally  Phujnician,  but  changed  by  the 
Greeks;  (3)  U  (same  as  V)  and  X,  invented  by  the  Greeks; 
(4)  C  and  F,  Phoenician  letters,  changed  in  value ;  (5)  G,  of 
Latin  invention  ;  (6)  Y,  introduced  into  Latin  from  the  Greek, 
with  changed  form;  (7)  J  and  V,  graphic  Latin  forms  varied 
to  independent  letters ;  (8)  W,  a  recent  addition,  formed  by 
doubling  U  or  Y,  whence  its  name. 

Capitals  and  Small  Letters. — In  ancient  Greek  writing, 
che  capital  letters  were  principally  used,  and  with  no  division 
marked  between  the  words.  The  small  cursive  character  was 
introduced  during  the  eighth  century,  though  the  introduction 
must  have  been  gradual ;  for,  in  the  oldest  Greek  manuscripts, 
even  as  early  as  the  fifth  century,  they  appear  intermixed  with 
capitals. 


222  METHODS   or  TEACHING. 

Vowels  and  Consonants — The  Phoenician  alphabet  con- 
sisted of  28  letters,  none  of  which  were  vowels.  They  em- 
ployed hardly  any  vowel  signs.  In  Hebrew,  the  three  princi- 
pal sounds,  a,  i,  u,  were  sometimes  expressed  in  writing,  and 
long  I  and  u  were  denoted,  not  b}'  special  signs,  but  by  con- 
sonants akin  to  them ;  a  was  regularly  omitted  except  at  the 
end  of  a  word,  where  it  was  denoted  by  He,  and  sometimes  by 
Aleph.  In  fiict,  in  all  Semitic  languages,  the  practice  was  to 
ignore  vowels  in  writing,  leaving  it  to  the  reader  to  fill,  ac- 
cording to  the  context,  the  unvarying  framework  of  conso- 
nantal sounds.  The  Hebrew  vowel  points  were  a  later  invention, 
rendereil  necessary  when  the  language  ceased  to  be  spoken. 

JJirecfiun  of  ll'ritlny. — The  direction  of  writing  varied 
among  the  dirterent  nations  of  antiquity  ;  but  in  general  the 
Semitic  races  wrote  from  right  to  left  and  the  Aryan  from  left 
to  right.  The  early  Greeks,  like  the  Phcenicians  and  other 
eastern  nations,  originallv  wrote  from  right  to  left.  Subse- 
(piently  the^'  wrote  consecutivel}'  from  right  to  left  and  left  to 
right,  as  land  is  plowed,  the  writing  being  called  furroweJ 
writing.  This  melhoil  was  continued  for  a  long  time;  the 
laws  of  Solon,  promulgated  594  B.  C,  were  written  thus;  and 
it  was  used  uuUl  the  tifth  century  B.  C.  AVriting  from  left  to 
right  was  introduced,  however,  before  the  alternate  method 
was  aban<lone(l ;  inscriptions  dated  742  B.  C.  have  been  found 
written  fi'om  left  to  right ;  and  Herodotus  speaks  of  the 
method  of  writing  from  left  to  right  as  the  established  cus- 
tom  of  the  Greeks  in  his  time. 

The  Chinese  and  Japanese  write  in  columns,  beginning  at 
the  top  and  passing  from  right  to  left.  The  Mexican  picture- 
writing  was  also  in  columns,  and  read  from  the  bottom 
upward.  The  Egyptian  hierogh'phics  are  sometimes  without 
au3'  arrangement,  but  are  generally  written  either  in  columns 
or  horizontal  lines,  according  to  the  shape  of  the  surface  to  be 
inscribed.  The  cuneiform  inscriptions  are  always  from  left  to 
light. 


TEACHING   THE   ALPHABET.  123 

II.  Methods  of  Teaching  the  Alphabet. 

After  pupils  have  learned  to  read  little  sentences,  and  have 
analyzed  spoken  words  into  their  elements,  the  elementary 
sounds,  and  written  -words  into  their  elements,  letters,  these  let- 
ters and  their  names  are  to  be  taught ;  and  we  will  now  proceed 
to  consider  the  ways  in  which  it  may  be  done. 

It  will  be  noticed  that  there  is  a  difference  between  knowing 
the  letters  and  knowing  their  names.  In  teaching  children 
the  sounds  of  the  letters  before  their  names,  they  will  have 
become  familiar  with  the  forms  of  the  letters  before  they  know 
what  to  call  them.  Indeed,  if  they  were  asked  their  names, 
they  would  no  doubt  give  the  sound  of  the  letter  as  the  name 
of  it. 

The  Methods. — The  alphabet  may  be  taught  with  a  Book, 
with  Cards,  and  with  Slate  and  Blackboard.  Each  of  these 
methods  has  its  advantages,  and  they  may  all  be  used  by  the 
teacher. 

With  a  Sooh. — The  old  method  of  teaching  the  alphabet 
was  to  begin  at  A  and,  the  teacher  pointing  with  a  knife  or 
pen,  have  the  pupil  go  all  the  way  down  to  Z,  and  then  go 
back  again  up  to  A.  Sometimes  there  would  be  a  little 
"  skipping  around"  among  the  letters,  and  occasionally  an 
effort  made  to  fix  some  particular  letter  in  the  memory  of  the 
child.  Two  such  lessons  in  the  forenoon  and  two  in  the  after- 
noon constituted  the  entire  work  of  the  primary  pupils  in  our 
public  schools  thirty  or  forty  years  ago ;  and  it  is  said  that 
this  method  is  not  yet  obsolete.  It  often  required  several 
months  for  the  pupil  to  learn  all  the  letters  when  taught  by 
this  method.  Pupils  were  frequently  known  to  be  able  to 
repeat  all  the  names  of  the  letters  in  their  order  without  know- 
ing the  letters  to  which  the  names  belonged. 

The  correct  method,  in  teaching  with  the  Book,  is  to  select 
some  of  the  most  easily  remembered  forms,  as  o,  a;,  i,  etc.,  call 
attention  to  the  peculiarities  of  their  form,  and  thus  impress 


124  METHODS   OF   TEACHING. 

them  and  their  names  on  the  memory.  Teach  a  few  letters 
the  first  day,  review  these  and  add  a  few  more  the  next  day, 
and  thus  continue  until  all  are  learned.  In  this  way  the  entire 
alphabet  can  be  taught  in  a  very  few  days. 

An  advantage  of  the  pupils  having  books  is  that  they  may 
have  them  at  their  seats,  and  look  at  the  letters  when  not  re- 
citing, and  thus  become  familiar  with  their  forms.  They  may 
thus  also  print  the  letters  from  their  l)ooks  on  their  slates, 
which  will  impress  their  forms.  Another  advantage  is  that 
the}'  may  take  their  books  home  and  get  some  instruction 
from  their  brothers  and  sisters  or  their  parents.  An  objection 
to  the  use  of  the  book,  as  compared  with  the  use  of  cards,  is 
that  it  does  not  admit  of  classification ;  only  one  or  two  can 
thus  recite  at  a  time. 

With  Cards. — We  may  also  teach  the  alphabet  by  the  use 
of  Cards.  To  teach  by  this  method  we  need  a  set  of  cards. 
These  cards  should  be  large,  containing  letters  printed  on 
them  in  large  type.  The  first  card  of  the  set  should  have 
some  of  the  more  easily  learned  letters,  as  0,  X,  S,  etc., 
printed  near  its  centre,  and  the  same  letters  in  connection 
with  others  in  the  margin.  The  next  card  should  contain 
more  new  letters  in  the  centre,  and  these  and  those  already 
learned  be  combined  with  others  in  the  margin.  The  letters 
should  also  be  combined  in  words,  both  near  the  centre  of  the 
card  and  in  the  margin  of  it. 

The  teacher  will  call  attention  to  some  letter,  as  o,  talk 
about  it,  awaken  an  interest  to  know  its  name,  and  then  give 
the  name  and  have  the  pupils  repeat  it.  Do  the  same  with 
another  letter  and  another,  until  he  has  taught  as  many  in  one 
lesson  as  he  thinks  the  pupils  can  remember.  He  may  then 
send  some  one  to  the  card  to  point  out  the  letters  as  he  names 
them ;  or  he  may  have  the  class  name  them  as  he  points  them 
out. 

He  may  then  have  the  pupils  search  for  some  of  the  letters 
in  the  margin  of  the  card  where  the}^  are  mixed  with  other 


TEACHING   THE   ALPHABET.  125 

letters.  A  little  competitive  trial  of  skill  may  be  had  to  see 
■who  will  find  the  most  letters  in  the  margin.  Such  an  exercise 
Dr.  Wickersham  describes  under  the  head  of  "  hide  and  seek" 
with  letters.  A  high  degree  of  interest  can  be  aroused  in  this 
way. 

The  advantage  of  the  Card  Method  is  that  it  admits  of  clas- 
sification. A  dozen  or  more  can  recite  at  the  same  time.  It 
also  excites  a  deep  interest  on  account  of  its  allowing  a  com- 
petitive trial,  which  makes  the  lesson  attractive  and  aids  in 
fixing  the  forms  and  names  in  the  mind.  It  has  the  disadvan- 
tage,  compared  with  the  Book  Method,  of  not  being  accessi- 
ble to  the  children  at  their  seats  or  at  home.  It  should  be 
used  in  connection  with  the  book  method. 

Slate  and  Blackboard. — The  Slate  and  Blackboard  may 
be  used  in  teaching  the  alphabet.  In  teaching  the  letters  in 
this  way,  the  teacher  should  go  to  the  board  and  print  the 
letter  neatly  upon  it ;  and,  calling  attention  to  the  peculiarity 
of  its  form,  as  before  suggested,  show  the  pupils  how  he  makes 
it,  and  give  them  its  name.  He  should  then  require  the  pupils 
to  make  the  letter  upon  the  slate  or  blackboard,  correcting 
their  errors,  and  showing  how  to  improve  its  form.  He 
should  proceed  in  this  way  with  all  the  letters,  beginning  as 
before  with  the  most  easily  remembered. 

There  are  several  letters  which  it  is  difficult  for  pupils  to 
distinguish  from  one  another,  that  ma}'  be  best  taught  by  this 
method.  The  principal  of  these,  among  the  small  letters,  are 
6,  (Z,  p,  and  q.  These  letters  may  be  divided  into  two  parts, 
called  the  curve  and  the  stem.  The  teacher  may  draw  a  stem 
on  the  board,  and  put  the  curve  first  in  one  place,  and  then 
another,  now  at  the  lower  right  hand  corner,  then  at  the  lowei 
left  hand  corner,  etc.,  requiring  the  pupil  to  give  the  name  of 
the  letter  thus  formed.  The  blackboard  can  also  be  advanta- 
geously used  in  teaching  pupils  to  distinguish  such  letters  as 
c  and  e,  n  and  m,  etc. 

One  advantage  of  the  slate  and  blackboard  method  is  that 


126  METHODS   OF   TEACHING. 

the  drawing  of  the  form  impresses  the  form  on  the  mind. 
Another  advantage  is  that  it  affords  pleasant  employment  for 
the  pupils  when  at  their  seats.  In  order  to  have  them  draw 
when  not  reciting,  the  teacher  ma}'  print  large  letters  on  the 
board  for  them  to  copy,  or  they  may  copy  from  their  cards  or 
their  books. 

General  Hemarks. — Children  at  home  ma}'  have  blocks 
with  the  letters  on  them ;  but  these  will  not  be  found  very  con- 
venient in  a  public  school.  A  Reading  Frame,  consisting  of 
an  upright  frame  on  which  strips  are  fastened,  forming  grooves 
in  which  blocks  containing  letters  maj'  be  placed,  is  also 
recommended,  and  ma}'  be  used  in  a  primary  school  with  ad- 
vantage. It  is  not  needed,  however,  in  an  ordinary  public 
school. 

Should  the  small  letters  or  the  capitals  be  taught  first?  The 
old  custom  was  to  teach  the  capitals  first ;  but  it  is  now 
thought  that  the  small  letters  should  be  taught  before  the 
capitals.  This  is  almost  a  necessity,  if  we  teach  pupils  words 
before  letters,  and  analyze  words  into  their  letters,  as  words 
in  their  ordinar}'  form  are  printed  in  small  letters.  But  even 
if  letters  were  taught  before  words,  the  small  letters  should 
be  taught  first,  since  we  should  immediately  unite  the  letters 
into  words.  Besides  this,  when  pupils  are  taught  the  small 
letters,  they  will  learn  the  capitals  almost  without  any  instruc- 
tion. 

Finally,  remember  that  the  pupils  should  be  taught  to  re- 
peat the  letters  in  their  proper  order.  This  will  be  needed  in 
consulting  the  dictionary,  and  for  many  other  purposes. 


CHAPTER  IV. 

TEACHING   PRONUNCIATION. 

PRONUNCIATION  consists  in  the  correct  utterance  of 
words.  The  term  pf^onunciation  is  derived  from  pro, 
forth,  and  nuncio,  I  announce;  and  means,  literally,  a  speak- 
ing; forth. 

Words  may  be  pronounced  upon  seeing  the  charactei-s 
which  compose  them,  or  upon  hearing  uttered  tiie  names  of 
the  characters,  or  the  sounds  represented  by  the  characters. 
In  reading,  we  pronounce  words  upon  seeing  the  characters 
which  compose  ihcia.  If  the  letters  of  a  familiar  word  be 
named  to  us  in  their  order,  or  if  the  sounds  of  any  word  be 
thus  given,  we  can  pronounce  the  word. 

I.   Nature  and  Importance. 

The  pronunciation  of  the  English  language,  like  that  of  all 
living  languages,  is  in  a  great  measure  arbitrar3\  It  is  liable 
to  change  from  one  age  to  another  ;  and  varies  in  different 
countries  where  it  is  spoken,  and  in  different  divisions  of  the 
same  country.  Even  people  of  the  same  place  differ  in  the 
pronunciation  of  man}'  words,  influenced  by  the  caprices  of 
fashion  and  taste. 

The  standard  of  pronunciation  is  the  present  usage  of  lite 
rary  and  cultivated  society.  In  England,  the  usage  of  the 
best  soeiet}'  of  London  is  regarded  as  the  principal  standard, 
thougli  the  usage  of  good  society  in  that  city  is  not  uniform 
We  have  no  one  city  in  this  countr}'  which  holds  a  correspond- 
ing rank  as  a  centre  of  intelligence  and  fashion,  and  thus  no 
special  standard  of  usage  to  govern  us.  American  scholars 
are,  however,  largely  influenced  by  English  custom. 

(127) 


128  METHODS   OF   TEACHING. 

A  standard  dictionary  should  aim  to  present  the  best  usage 
of  the  present  time.  The  standard,  therefore,  for  students,  is 
the  standard  dictionary.  The  standard  dictionaries  of  this 
country  are  Webster  and  Worcester.  Where  they  agree,  we 
have  a  guide  which  we  ma}^  follow  with  entire  confidence. 
Where  they  differ,  we  must  decide  by  the  custom  of  the  best 
speakers  that  we  hear,  or  by  other  information  that  we  may- 
possess.  Of  course,  we  have  excellent  authority  for  our  usage, 
if  we  follow  either  one  of  these  dictionaries. 

It  is  a  good  rule  not  to  ditfer  from  those  with  whom  we  as- 
sociate any  further  than  correct  usage  actually  requires.  It 
seems  like  an  affectation  to  use  a  pronunciation  different  from 
our  associates,  when  theirs  is  also  supported  by  good  author- 
it3^  For  an  American  to  say  either  {ither)  and  neither 
(ni  ther)  in  society  when  these  words  are  pronounced  accord- 
ing to  the  usual  custom  e  ther  and  ne  ther,  is  an  inexcusable 
affectation.  We  should  always  remember,  also,  that  though 
our  own  pronunciation  is  right,  another  person's  may  not  be 
wrong  when  it  differs  from  ours.  The  pronunciation  of  words 
is  not  a  matter  of  absolute  right,  but  of  taste  and  culture. 

The  pronunciation  of  the  English  language  is  very  difficult. 
This  difficulty  arises  partly  from  the  irregularity  of  our  or- 
thography, and  partly  from  the  carelessness  of  persons  in 
respect  to  pronunciation.  Many  persons  pronounce  incor- 
rectly a  large  number  of  the  words  they  use  in  ordinary  con- 
•/ersation ;  and  very  few  persons  can  read  a  page  of  an  ordi- 
nary book  without  several  mispronunciations.  Indeed,  it  is 
an  exceptional  thing  to  listen  to  a  public  speaker  who  does 
not  make  many  mistakes  of  this  kind  in  an  hour's  address. 

The  correct  pronunciation  of  words  does  not  receive  the 
attention  which  its  importance  demands.  Men  who  would 
blush  at  a  mistake  in  grammar,  or  feel  deeply  mortified  at  the 
misspelling  of  a  word,  go  on,  year  after  year,  mispronouncing 
many  of  the  ordinary  words,  with  apparent  indifference,  and 
with  no  effort  at  correcting  their  mistakes.     Such  mistakes  as 


TEACHING    PRONUNCIATION.  129 


i' 


dea  for  ide'a,  complex'  for  com'j^lex,  in'quiry  for  inqui'rxj^ 
and  the  incorrect  sounds  of  the  vowel  in  such  words  as  food^ 
root,  half,  past,  etc.,  we  hear  constantl}'  made  b}'  educated 
men,  who  thus  show  their  hick  of  literarj'  culture  and  refine- 
ment. 

Correct  pronunciation  is  of  even  greater  importance  than 
correct  spelling,  since  we  make  constant  and  dail}'  use  of 
spoken  words,  while  we  write  much  less  frequentl}-.  A  mis- 
spelled word  is  an  offence  to  the  eye,  but  a  mispronounced 
word  is  an  offence  to  the  ear ;  and  the  ear  is  as  delicate  and 
refined  as  the  e3'e.  It  should  be  regarded  as  less  displeasing 
to  see  a  misspelled  word  in  a  person's  letter  than  to  hear  a 
mispronounced  word  in  his  conversation  or  speech. 

Teachers  should  be  especiall}^  particular  in  respect  to  pro- 
nunciation. They  should  be  careful  that  they  pronounce  cor- 
rectly as  a  model  for  their  pupils  to  imitate.  They  should 
make  constant  eftbrts  to  correct  the  mistakes  of  their  pupils, 
and  to  train  them  to  pronounce  correctly.  It  is  not  sufficient 
that  attention  be  called  to  their  mistakes ;  but  pupils  should 
be  drilled  on  the  mispronounced  words  until  they  have 
acquired  the  habit  of  pronouncing  them  correctly.  Pupils 
should  be  required  to  keep  a  list  of  the  words  which  they  mis- 
pronounce, and  be  frequently  drilled  upon  them. 

II.   Methods  of  Teaching. 

There  are  two  distinct  methods  of  teaching  the  pronuncia- 
tion of  words,  called  the  Associative  Method  and  the  Phonic 
Method.  Both  of  these  have  already  been  referred  to  in  teach- 
ing a  child  to  read ;  they  will  now  be  discussed  more  fully. 

The  Associative  Method — The  Associative  Method  con- 
sists in  teaching  the  pronunciation  of  words  by  leading  the 
pupil  to  associate  the  name  of  the  word  with  its  form.  This 
is  the  method  by  which  we  begin  to  teach  a  little  child  to  read. 
The  pupil  sees  the  word,  the  teacher  gives  its  name,  and  the 
6* 


130  METHODS   OF   TEACHING. 

pupil  is  required  to  associate  the  name  with  the  form  and 
remember  it,  just  as  he  learns  the  name  of  any  other  object. 
In  this  way  a  child  learns  to  pronounce  woi'ds  before  it  knows 
its  letters. 

This  is  the  correct  method  for  the  beginner.  First,  it  is  the 
natural  method  ;  it  is  the  same  way  in  which  we  begin  spoken 
language,  and  in  which  we  learn  the  names  of  other  objects. 
It  is  also  the  most  interesting  method  ;  for  a  3'oung  pui:)il  is 
more  interested  in  words  than  in  abstract  characters.  It  is 
the  most  philosophical  method,  for  it  proceeds  from  the 
known  to  the  unknown,  from  the  known  spoken  word  to  the 
unknown  written  word.  It  is  also  the  historic  method ;  for 
written  language  employed  symbols  for  entire  words  before 
it  used  letters  ;  and  the  historical  oi'der  of  development  gen- 
erally indicates  the  true  order  for  the  child. 

The  associative  method,  however,  has  its  limitations.  The 
pupil  can  pronounce  only  the  words  which  have  been  pro- 
nounced for  him.  Each  new  word  must  be  named  for  him 
before  he  can  pronounce  it.  He  attains  no  knowledge  by 
which  he  can  pronounce  new  words  independently  of  the 
teacher.  It  therefore  needs  to  be  supplemented  by  some 
other  method  by  which  the  pupil  can  learn  to  pronounce  new 
words  for  himself.  This  method  is  the  Phonic  Method,  which 
we  shall  now  consider. 

The  Phonic  Method. — The  Phonic  Method  of  teaching 
pronunciation  is  that  b}'^  which  we  teach  pupils  to  pronounce 
words  b}'  combining  their  elementary  sounds.  By  this  method 
we  first  teach  the  pupils  the  elementary  sounds,  then  the 
characters  which  represent  these  sounds,  and  then  lead  the 
pupil  to  combine  the  sounds  in  their  order  as  he  sees  the 
letters. 

Were  the  English  language  phonetic,  this  method  would  be 
entirely  simple  and  easy.  Having  learned  the  sounds  and  the 
characters  representing  them,  the  pupil  would  be  able  to  pro- 
nounce, with  a  little  practice,  any  word  he  might  see.     A  Ian- 


I 


TEACHING   PRONUNCIATION.  131 

o-uao-e  is  phonetic  when  it  has  a  character  to  represent  each  ele- 
mentary sound,  when  each  elementar^y  sound  is  represented  by 
but  one  character,  and  when  words  are  spelled  as  pronounced 
and  pronounced  as  spelled.  The  English  language  is  not  pho- 
netic :  hence  this  general  method  becomes  somewhat  modified 
in  its  application,  and  its  difficulties  are  increased.  We  shall 
describe  how  the  method  may  be  applied  to  our  language. 

There  being  about  forty  sounds  in  the  language,  and  only 
twent3'-six  charactei's,  we  have  not  characters  enough  to  rep- 
resent all  the  sounds  ;  we  are  therefore  compelled  to  adopt 
some  notation  to  be  used  with  these  characters  to  indicate  the 
remaining  fourteen  sounds.  We  maj'  use  figures  as  exponents 
or  subscripts,  or  the  marks  in  some  standard  dictionar3\ 
Thus,ai  or  a^,  or  a  might  represent  the  first  sound  of  a;  a^,  or 
a 2,  or  d  might  represent  the  second  sound  of  a;  etc.  The 
different  sounds  of  the  consonants  may  also  be  indicated  by 
marks.  All  the  primary  readers  should  have  some  notation 
which  the  teacher  can  adopt  in  this  instruction. 

The  next  step  in  the  method  is  to  indicate  the  silent  letters, 
so  that  the  pupil  may  know,  on  seeing  a  word,  wliat  letters  to 
sound  and  what  not  to  sound.  This  may  be  done  by  print- 
ing the  silent  letters  in  a  lighter-faced  type  as  Dr.  Leigh  does, 
or  in  italics,  as  is  done  in  many  of  our  spelling-books  and 
readers,  or  with  a  stroke  across  them,  as  is  done  in  a  recent 
series  of  readers.  Thus  the  word  fate  might  be  printed  fate 
or  fate;  the  word  light^  light,  or  light. 

Having  received  this  instruction,  the  pupil  will  be  able, 
with  a  very  little  practice,  to  pronounce  all  new  words  that  he 
meets  in  his  readei's.  All  that  he  must  do  to  pronounce  a 
word  is  to  give  the  elementary  sounds,  as  indicated  by  its  let- 
ters, in  the  order  in  which  they  occur  in  the  word,  being  care- 
ful that  they  flow  naturally  and  musically  into  one  another. 
After  he  is  familiar  with  words  printed  in  this  way,  he  will 
experience  little  difficulty  in  recognizing  them  when  printed 
\n  the  usual  form. 


132  METHODS   OF   TEACHING. 

The  sounds  of  the  letters  may  also  be  indicated  by  using  the 
diacritical  marks  of  the  dictionary.  This  method  has  been  used 
by  many  teachers  with  great  success.  It  has  been  very  thor- 
oughly and  successfully  tested  in  many  of  the  schools  of  the 
country.  If  the  primer  or  primary  reader  used  in  the  school 
has  no  marks,  the  teacher  can  mark  the  words  neatly  with  pen 
or  pencil.  Nearly  every  series  of  readers  now  published  in  this 
country  has  a  system  of  marks  to  represent  the  sounds,  and  the 
teacher  can  adopt  the  system  of  the  books  he  uses. 

In  favor  of  the  Phonic  Method,  we  remark  that  it  is  natural, 
philosophical,  and  practical.  It  is  not  a  mere  theory ;  it  is  a 
method  of  great  practical  value.  It  is  not  an  untried  experi- 
ment ;  its  utility  has  been  demonstrated  by  the  test  of  our 
best  teachers.  No  intelligent  teacher  who  adopts  it  will  ever 
discontinue  its  use  ;  and  it  is  difficult  to  see  how  a  teacher  can 
be  intelligent  who  has  not  adopted  it.  The  indications  are 
that  it  will  soon  be  universally  adopted  in  this  country. 

Other  3Iefho(ls. — There  are  several  other  methods  that 
have  been  used  in  teaching  pronunciation,  the  most  prominent 
of  which  are  the  Alphabetic  and  Phonetic  Methods.  Besides 
these  there  are  several  modifications  of  the  Phonic  Method,  in 
which  special  forms  of  letters  are  suggested,  which  may  be 
included  under  the  general  name,  Typographic  Method. 

Alphabetic  Method. — The  Alphabetic  Method  is  that  in 
which  the  teacher  attempts  to  teach  pronunciation  by  having 
the  pupils  call  the  names  of  the  letters.  Thus  in  the  word 
fight^  the  teacher  has  the  pupil  say  e/",  eye,  ge^  aitch,  tee,  and 
then  pronounce  the  word  fight.  The  thought  was,  if  there 
was  any  thought  on  the  part  of  the  teacher,  that  the  naming 
of  the  letters  of  a  word  would  enable  the  pupil  to  pronounce 
the  word. 

This  method  was  formerlj^  the  only  one  used  in  our  schools. 
Nearly  every  adult  of  the  present  day  was  taught  to  pro- 
nounce words  in  this  way.  The  method,  however,  is  an  ab- 
surdity.   No  one  ever  actually  learned  to  pronounce  words  in 


TEACHING   PRONUNCIATION.  133 

Ihis  way,  though  teachers  have  attempted  to  teach  in  this 
way.  Children  who  were  required  to  learn  in  this  way,  act- 
ually learned  b}^  association  and  the  phonic  principle.  They 
heard  the  teacher  pronounce  the  words  several  times,  and 
remembered  the  pronunciation,  associating  the  name  of  the 
word  with  its  form.  They  also  unconsciously  acquired  a 
knowledge  of  the  powers  of  the  letters,  so  that  when  they  saw 
them  or  named  them  in  words,  the}'  knew  what  their  powers 
were.  They  were  often  guided  also  by  analogy  in  pronounc- 
ing similar  words. 

The  objection  to  the  method  is  that  the  name  of  the  letter 
is  not  its  sound.  In  many  cases,  the  name  not  onh'  does  not 
sus:s:est  the  sound,  but  bears  no  relation  to  it.  How,  for  in- 
stance,  can  any  learner  know  that  the  sounds  represented  by 
aitch^eye,  double  e/Z,  spell  the  word  hill.  If  we  should  pro- 
nounce words  by  uniting  the  names  of  their  letters  we  should 
have  quite  a  different  word  from  the  one  intended.  Thus  me 
would  spell  the  word  em-me,  at  would  spell  eigh-ty,  leg  would 
spell  el-e-gy,  ntt  would  spell  en-ti-ty,  iitk  would  spell  u-ti-ca. 
etc.,  and  what  the  names  of  the  letters  of  such  words  as 
brought  and  phthisic  would  spell,  we  leave  to  the  ingenuity  of 
the  teacher  who  still  uses  this  method.  A  method  so  evi 
dentl}'  absurd  should  no  longer  find  a  place  in  our  schools. 

Rev.  Thomas  Hill,  one  of  the  most  eminent  educators  of 
the  age,  says:  "  In  teaching  a  child  A,  B,  C,  and  impressing 
on  his  mind  that  these  letters  spell  the  words  of  the  language, 
you  teach  him  a  falsehood  and  give  him  little  chance  to  detect 
the  cheat.  I  say,  so  far  from  helping  him  to  read,  you  have 
put  a  formidable  obstacle  in  the  way  of  his  learning  to  read. 
The  letters  do  not  spell  the  words,  and  therefore  the  knowl- 
edge of  the  letters  does  not  aid  him  in  reading  the  words  ; 
they  do  spell  something  else,  and  therefore  are  an  actual 
hindrance  in  learning  to  read." 

Dr.  Currie  apologizes  for  those  who  use  it,  saying  that  "  it 
is  not  designed  to  be  a  reading  method  alone;  but  a  method 


134  METHODS   OF   TEACHING. 

for  teaching  reading  and  spelling  simultaneous!}'',  and  the 
reading  through  the  spelling."  He  also  says,  "It  does  not 
pretend  to  be  a  phonic  method,"  etc.  "  Yer^^  much  of  the 
argument  against  the  common  method  has  proceeded  on  the 
false  assumption  that  the  letter-names  of  a  word  and  its  sound 
are  set  forth  in  the  relation  of  phonic  parts  to  their  whole  ; 
and  has  therefore  not  touched  the  merits  of  the  question."  It 
is  clear,  however,  that  most  teachers  who  used  this  method  did 
so  to  teach  their  pupils  to  pronounce  words,  for  it  was  a 
common  tiling,  when  a  child  came  to  a  word  in  his  reading 
lesson  which  he  could  not  pronounce,  for  the  teacher  to  tell 
him  to  "  spell  the  word." 

JPhonetic  Metliod. — Another  method,  formei'ly  used  to 
some  extent,  is  that  which  has  been  called  the  Phonetic  Method. 
This  method  is  the  same  in  principle  as  the  Phonic  Method ;  it 
ditfers  from  it  in  introducing  about  fourteen  new  characters 
instead  of  using  a  notation ;  and  also  in  using  onl^'  the 
letters  in  spelling  a  word,  which  are  sounded  in  it. 

In  teaching  by  this  method,  the  elementary'  sounds  were 
taught,  then  the  twentj'-six  letters  as  representatives  of  twen- 
ty-six of  these  sounds,  and  then  about  fourteen  new  charac- 
ters to  represent  the  remaining  sounds.  Then  pupils  weiu 
taught  to  combine  these  characters  into  words,  using  only  as 
man}'  characters  in  spelling  a  word  as  there  are  elementarj' 
sounds  in  it.  Thus,  the  word  light  would  be  printed  lit;  hear, 
bar,  etc.  These  words  could  of  course  be  readily  pronounced 
by  the  pupil. 

Pupils  were  then  required  to  make  the  transition  from 
words  in  their  phonetic  forms  to  the  common  forms.  This 
was  done  by  having  words  in  the  two  forms  printed  in  parallel 
columns,  so  that  the  comparison  could  be  readil}-  made.  The 
word  in  the  phonetic  fornx  was  thus  a  sort  of  ke}'  to  the  pro- 
nunciation of  the  word  in  its  ordinary  form.  This  method, 
though  once  popular  with  a  certain  class  of  teachers,  is  now 
obsolete 


TEACHING   PRONUNCIATION.  •        135 

IIT.  Correct  Pronunciation. 

Having  shown  how  a  child  may  be  taught  to  pronounce 
words,  we  pass  on  to  consider  the  art  of  correct  and  artistic 
pronunciation.  Correct  pronunciation  includes  two  things; 
Articulation  and  Accent.  Ever}-  mistake  made  in  the  pro- 
nunciation of  a  word  is  an  error  of  either  articulation  or 
accent. 

Articulation. — The  basis  of  Pronunciation  is  Articula- 
tion. The  voice  must  be  moulded  into  the  elementar}- 
sounds  of  the  language,  as  a  primary  condition  of  expressing 
words.  This  moulding  of  the  voice  is  called  Articulation. 
Articulation  is  the  special  characteristic  of  human  speech  and 
of  mankind.  Man  is  the  only  animal  that  can  make  and  com- 
bine articulate  sounds. 

Nature  of  Articulation. —  Articulation  is  the  correct 
and  distinct  utterance  of  the  elementary  sounds  of  the  lan- 
guage. The  term  is  derived  from  articulus^  a  joint,  an  ar- 
ticulate sound  being  literally  a  jointed  sound.  Articulation 
differs  from  Pronunciation  as  a  part  from  the  whole  ;  for  while 
the  latter  refers  to  the  utterance  of  the  entire  word,  the  for- 
mer has  reference  to  the  utterance  of  the  elementary  parts  of 
a  word.  The  term  Enunciation,  from  e,  out  of,  and  nuncio^  I 
announce,  is  used  by  some  writers  as  synonymous  with  Articu- 
lation, and  by  others  as  meaning  the  utterance  of  the  element- 
ary sounds  as  combined  in  words. 

There  are  about  forty  elementary  sounds  in  the  English  lan- 
guage, though  orthdepists  are  not  agreed  with  respect  to  the 
exact  number.  Some  vowel  sounds,  which  are  regarded  as 
simple  by  one  writer,  are  shown  by  other  writers  to  be  a  com- 
bination of  two  simple  vocals.  Webster  and  Worcester  give 
about  forty  distinct  sounds,  and  this  is  sufficiently  correct 
for  all  practical  purposes. 

These  elementary  sounds  are  made  by  the  organs  of  the 
mouth  and  throat,  called  the  Organs  of  Speech.     The  organs 


136     '  METHODS   OF   TEACHING. 

of  speech  ma^^  be  regarded  as  a  set  of  flexible  moulds  which 
give  form  to  the  voice  which  flows  into  and  through  them. 
Any  imperfection  in  the  moulds  or  their  arrangement  will  tend 
to  impair  the  articulation.  In  order  to  articulate  correctly,  a 
person  must  possess  a  complete  control  over  these  organs,  so 
as  to  be  able  to  mould  the  voice  that  comes  up  from  the  larynx 
into  all  the  possible  forms  required. 

In  the  standard  dictionaries  all  the  sounds  of  the  language 
are  presented,  and  the  diacritical  marks  which  indicate  them. 
The  slight  shades  of  difierence  between  the  sounds  of  some 
of  the  vowels,  wlien  occup^Mng  different  places,  and  their 
modifications  by  being  associated  with  other  letters,  are  also 
explained.  All  of  this  knowledge  is  of  great  importance  to 
teachers,  and  sliould  be  thoroughly  mastered  by  them. 

The  importance  of  correct  articulation  is  very  great.  It  is 
the  basis  of  accurate  and  finished  utterance.  A  correct  and 
artistic  articulation  will  sometimes  atone  for  a  bad  voice. 
The  secret  of  the  power  of  Randolph's  oratory,  it  is  said,  lay 
in  his  articulation,  for  his  voice  was  creaking  and  disagreea- 
ble, but  by  culture  it  "became  so  fascinating"  that  it 
"haunted  the  hearer  like  the  spell  of  an  enchantress." 

Artistic  articulation  is  capable  of  producing  deep  and  vivid 
impressions  on  the  listener.  A  speaker  in  uttering  the  ex- 
pression "the  hiss  of  a  serpent,?'  by  slightly  prolonging  the 
final  sound  of  hiss  so  touched  the  imagination  of  one  of  his 
hearers  that  it  led  to  a  vivid  dream  of  a  serpent.  Prof. 
Thwing  mentions  a  speaker  who  just  before  his  departure  for 
the  Pacific  coast,  in  an  address  spoke  of  "the  wash  of  its 
waves,"  and  by  giving  a  slight  fullness  to  sh,  made  an  impres- 
sion on  his  mind  that  he  says  he  has  never  forgotten. 

Metuods  of  Teaching. — Correct  Articulation  is  taught  in 
three  ways :  by  Imitation^  by  Phonic  Analysis,  and  by  Cor- 
recting the  Errors  of  pupils. 

Iinifatioa. — The  pupil  learns  Articulation  principally  by 
imitation.     The  child  will  naturally  speak  like  his  parents  and 


TEACHING   PRONUNCIATION.  137 

eouiDanions.  If  their  enunciation  is  pure  and  correct,  bis  will 
be  pure  and  correct  also;  if  theirs  is  incorrect,  his  will  also 
be  incorrect.  Pupils  will  also  imitate  their  teacher;  he  should 
therefore  be  exceedingly  careful  that  he  presents  a  model  of 
correct  and  elegant  enunciation. 

Phonic  Atiali/sis. — Pupils  should  also  have  dail}'^  drill  on 
the  elementary'  sounds.  The  ear  thus  acquires  a  correctness 
and  delicacy  of  perception,  and  the  organs  are  trained  to  give 
accurately,  promptly,  and  with  ease,  all  the  sounds  of  the  lan- 
guage. Especial  drill  should  be  given  upon  the  more  difficult 
sounds  and  those  we  are  most  liable  to  2;et  wrong.  Words 
should  be  given  for  the  pupils  to  analyze  into  their  elementary 
sounds.     Such  a  drill  has  been  called  Phonic  Analysis. 

Fhonic  Analt/!<is  should  receive  the  careful  attention  of  the 
teacher.  It  is  the  foundation  of  all  distinct  articulation  and 
correct  pronunciation.  Many  of  the  faults  of  pronunciation, 
so  frequently  met  with,  may  be  prevented  or  removed  by  per- 
sistent drilling  on  the  elementary  sounds.  Phonic  Anah'sis 
should  include  an  exercise  on  the  vocals,  subvocals,  and  aspi- 
rates, by  themselves  and  in  combination.  Great  variety-  can 
be  given  to  the  exercises,  and  a  ver^-  great  degree  of  interest 
aroused  in  the  subject.  Phonic  analysis  should  not  be  re- 
stricted to  the  lower  grades,  but  should  constitute  a  part  of 
the  instruction  in  reading  or  elocution  in  every  stage.  The 
vocal  organs  need  constant  technical  exercise,  like  the  fingers 
of  a  pianist  or  violinist,  that  they  may  perform  their  offices 
with  ease,  accurac}',  and  artistic  excellence. 

Care  should  be  taken  to  correct  the  errors  of  omission,  as 
well  as  those  of  commission.  We  often  suppress  sounds  as 
Avell  as  make  incorrect  ones.  The  ear  should  be  trained  to 
distinguish  all  the  finer  shades  of  diiference  in  sounds ;  and  the 
organs  of  speech  should  be  carefully  trained  until  they  are  able 
to  produce  promptly  and  with  ease  all  the  sounds  of  the  lan- 
guage, in  all  their  varied  and  complex  combinations.  And 
Miie  can  best  be  attained  by  the  exercises  in  Fhonic  Analysis. 


138  METHODS    OF   TEACHING. 

"Words  and  sentences  containing  difficult  combinations 
should  be  repeated.  Take  such  words  as  strength,  shrubs, 
stretched,  etc.  Practice  also  uttering  difficult  sentences,  such 
as  "She  sells  sea-shells,"  "I  saw  six  slim  saplings,"  "There 
were  three  gray  geese  and  three  gray  ganders,"  "Around  the 
rugged  rock,  the  ragged  rascal  ran."  Pupils  may  be  required 
to  repeat  the  well  known  combinations,  "  Peter  Piper"  "The- 
ophilus  Thistle,"  "  Amidst  the  mists,"  etc.  A  drill  of  a  few 
minutes  each  day  on  such  exercises  will  be  foimd  to  be  of  great 
value  to  pupils.  The  words  should  be  repeated  as  rapidly  as 
they  can  be  spoken  with  distinctness.  Such  a  drill  can  be 
given  to  each  reading  class,  or  the  entire  school  may  have 
an  exercise  for  two  or  three  minutes  once  or  twice  a  day. 

Errors  of  Articulation. — There  are  several  special  defects 
in  articulation,  the  most  prominent  of  which  are  Stammering, 
Lisping,  and  Bad  Habits. 

Stammering. — Stammering  is  a  hindered  or  obstructed 
utterance  of  words.  It  is  due  to  various  causes,  which  should 
be  understood,  in  order  to  overcome  it.  Sometimes  it  is  the 
result  of  some  peculiarity  of  the  vocal  organs,  and  can  be 
cured  by  speaking  with  a  marble  or  pebljle  in  the  mouth. 
Demosthenes  is  said  to  have  overcome  a  defect  in  enunciation 
by  declaiming  with  pebbles  in  his  mouth. 

Sometimes  stammering  is  merely  a  habit  acquired  by  asso- 
ciating with  companions  who  stammer.  Sometimes  it  is  the 
result  of  rapid  and  heedless  talking.  Sometimes  it  is  the 
result  of  an  exuberance  of  feeling,  as  persons  often  stammer 
when  excited  or  angry.  In  these  cases,  care  on  the  part  of 
the  pupil  to  speak  slowly  and  with  deliberation,  will  be  suffi- 
cient to  overcome  the  habit.  Sometimes  stammering  is  due 
to  timidity  on  the  part  of  a  nervous  or  sensitive  pupil,  in 
which  case  the  teacher  should  endeavor  to  cfive  him  confi- 
deuce  in  himself,  and  make  him  feel  at  ease. 

More  frequently,  stammering  arises  from  some  peculiarity 
of  the  nervous  system,  either  natural  or  the  result  of  disease. 


TEACHING   PRONUNCIATION.  139 

The  great  remedy  in  such  cases  is  speaking  slowly.  We  have 
known  persons  to  be  cured  by  practicing  talking  "to  time," 
beating  time  with  the  finger  and  speaking  their  words  at 
measured  intervals.  The  nervous  system  seems  to  respond 
to  the  rhythmical  movement,  as  is  seen  in  the  fact  that  per- 
sons who  stammer  when  they  talk  or  read,  will  not  stammer 
in  singing.  For  the  same  reason  it  will  be  found  that  pupils 
who  stammer  read  poetry  more  easily  than  prose.  Another 
suggestion  is  that  the  pupil  accustom  himself  to  a  clear  idea 
of  what  he  is  to  say  before  he  begins  to  speak.  Deliberation 
and  confidence  are  essential  elements  of  a  cure  in  nearly-  every 
case.  An  intelligent  common  school  teacher  can  usually  cure 
the  most  inveterate  cases  of  stammering,  if  he  will  pei'severe 
in  the  attempt,  and  is  able  to  secure  the  assistance  of  the  pupil. 

Lisping. — Lisping  is  mainly  the  use  of  the  sound  Ih  for  s. 
It  is  a  habit  found  more  frequentl}^  among  girls,  as  stammer- 
ing is  more  frequent  among  boys.  Sometimes  it  is  a  mere 
affectation  of  speaking,  in  which  case  it  can  be  cured  b}'  show- 
ing the  pupil  how  it  mars  the  speech,  and  perhaps  by  using  a 
little  judicious  ridicule. 

More  frequently,  lisping  is  a  natural  defect  of  enunciation, 
caused  hy  some  peculiarity  of  the  organs  of  speech.  Occa- 
sionally it  is  due  to  the  tongue  being  a  little  large,  or  a  little 
too  long.  A  person  will  sometimes  lisp,  also,  when  the  front 
teeth  are  ver}-  large  or  ver^^  prominent.  To  correct  the  habit, 
in  these  cases,  the  pupil  must  first  be  led  to  notice  the  defect 
in  his  articulation ;  a  person  sometimes  lisps  and  is  not  aware 
of  it.  The  pupil  must  then  be  shown  the  positions  of  the 
organs  in  making  the  sound  of  s,  and  the  sound  of  th,  and  be 
carefull}'  drilled  on  these  two  sounds,  and  then  on  words  con- 
taining the  sound  of  s,  until  thej'  can  be  correctly  pronounced. 
It  often  requires  persistent  practice  to  overcome  the  defect, 
but  it  should  be  continued  until  cured. 

Bad  Habits. — Pupils  often  acquire  the   habit  of  incorrect 
or  imperfect  articulation  by  carelessness  in  talking,  or  by  the 


140  METHODS    OF    TEACHIXQ. 

imitation  of  incorrect  forms  of  speech  common  in  their  neigh- 
borhood. Such  words  as  which ^  where^  when,  etc.,  are  very 
generally  mispronounced  by  omitting  the  sound  of  A,  which, 
though  written  after  the  w,  is  sounded  before  it.  Tlie  words 
shrub  and  shrink^  pronounced  sj'ub  and  srink,  illustrate  the 
same  error.  Final  ing  is  often  abbreviated  to  in;  as  nothing, 
something,  etc.,  called  nolhin,  somethin,  etc.  There  are  hun- 
dreds of  such  errors,  which  teachers  should  notice  and  try  to 
correct. 

Some  of  the  most  common  errors  of  articulation  found  in  the 
public  schools  of  several  States  are  those  which  arise  from  tlie 
early  use  of  the  German  language.  We  call  attention  to  some 
of  the  most  prominent  of  these  errors.  Pupils  confound  the  « 
and  z,  calling  is,  iss  instead  of  iz;  his,  hiss  instead  of  hiz,  etc. 
They  confound  v  and  w,  saying  wine  for  vine,  and  vine  for 
wine,  etc.  They  confound  s  and  /7i,  saying  wis  for  with,  sin 
for  thin,  thick  for  sick,  etc.  They  confound  ch  and,/,  as  jurch 
for  church,  chug  for  jug,  Chan  for  John,  etc.  They  confound 
d  and  t,  as  "  toivn  the  hill"  for  "down  the  lull,"  and  "I  can't 
to  it"  for  "I  can't  do  it;"  they  confound  d  and  th,  as  den  for 
then,  and  even  b  and  p  as  bray  for  pray,  prick  for  brick. 

In  New  England  there  is  a  peculiarity  of  pronunciation 
which  consists  in  adding  the  sound  of  r  to  the  end  of  words 
ending  with  the  Italian  sound  of  a,  as  idear,  arear,  etc.  At 
the  same  time,  there  is  a  tendency  to  omit  the  sound  of  r  at 
the  end  of  words;  as,  watah  for  water,  daughtah  for  daughter ; 
and  to  omit  or  soften  the  r  in  other  places ;  as  New  Yawk  for 
New  York,  etc.  This  peculiarity  reminds  one  of  the  English- 
man's trouble  with  his  Ti's,  his  tendency  being  to  use  the  h 
where  it  does  not  belong,  and  to  omit  it  where  it  does  belong, 
saying  ^ouse  for  house  and  hobject  for  object.  Many  other 
States,  though  not  presenting  so  striking  a  peculiarity  as 
the  New  Englander's  r,  have  much  more  serious  defects  in  the 
articulation  of  their  people. 

To  overcome  these  bad  habits,  two  things   are  required. 


TEACHIXG   PROXUNCIATION.  141 

First,  the  pupil  must  be  led  to  perceive  that  he  makes  the 
mistake ;  the  ear  must  be  trained  to  detect  the  difference  of 
the  sounds,  and  to  notice  when  the  incorrect  one  is  given. 
Second,  the  pupil  must  be  taught  the  position  of  the  organs 
in  making  the  sounds,  and  be  drilled  upon  them  until  he  can 
make  them  at  his  will.  Then  it  will  require  constant  atten- 
tion on  the  part  of  both  teacher  and  pupil  in  order  to  break 
awa}^  from  the  old  habit  and  acquire  the  new  one. 

Besides  these  special  errors,  there  is  a  class  of  general  ones 
that  demand  notice.  The  word  and  is  badly  abused  in  pro- 
nunciation, often  being  passed  by  "  with  merely  an  uncourteous 
nasal  salute."  The  terminations  ness  and  less  are  often 
changed  to  niss  and  liss^  ment  to  munt,  and  oic  into  er,  as 
feller  for  fellow,  piller  for  pillow,  etc.  Words  are  marred  also 
bj''  the  omission  of  sounds  :  as  histry  for  history,  evry  for 
every,  reglar  for  regular,  Fehuary  for  February,  etc. 

Accent. — The  second  condition  for  correct  pronunciation 
IS  Accent.  When  the  elementary  sounds  are  made  correctly, 
and  the  stress  of  voice  falls  on  the  proper  syllable,  the  word 
is  pronounced  correctly.  We  shall  speak  of  the  Nature  of 
Accent,  and  Methods  of  Teaching  it. 

Nature  of  Accent. — Accent  is  a  stress  of  voice  upon  one 
or  more  syllables  of  a  word.  The  term  is  derived  from  the 
Latin,  ad,  to,  and  cantus,  a  song,  showing  that  accent  was 
primarily  related  to  singing. 

Accent  gives  a  musical  element  to  speech,  and  adds  to  the 
beauty  and  harmony  of  language.  The  ancient  languages  dis- 
tinguished syllables  by  what  is  called  quantity;  that  is,  as 
long  and  short  syllables.  The  French  language  is  so  nearly 
deficient  in  accent  that  blank  verse  is  an  impossibilit}-  in 
French  literature. 

Accent  is  of  two  kinds.  Primary  and  Secondary.  Primary 
Accent  is  the  stronger  accent  in  pronouncing  words ;  Second- 
ary Accent  is  the  weaker  or  slighter  accent  in  pronouncing 
words.     In  some  words  the  secondar}'  accent  is  almost  as 


142  METHODS   OF   TEACHING. 

strong  as  the  primaiy;  as,  violin,  caravan,  artisan,  etc. 
Some  words  have  two  secondary  accents  ;  as,  incotnprehensi- 
oility  and  antipestilential.  The  word  amen  has  both  syllables 
accented  :  and  man}^  compound  words  have  a  slight  secondary 
accent,  as  gain-say,  light-house,  etc. 

The  primarj'  and  secondary  accents  are,  in  man}-  cases,  so 
nearly  equal  that  they  are  frequently  exchanged,  the  primary 
becoming  secondary,  and  the  secondary  primary.  Many 
words,  such  as  ar'tisan,  rev'erie,  in'valid,  etc.,  have  trans- 
ferred the  primary  accent  from  the  last  to  the  first  syllable. 

All  words  in  the  English  language  of  more  than  one  sylla- 
ble have  one  accented  syllable  ;  and  most  pol^'s^dlabic  words 
have  a  primary  and  a  secondary  accent.  It  is  a  general  ten- 
dency of  the  language  to  place  the  accent  on  the  first  syllable 
of  dissyllables,  and  on  the  antepenult  of  polysyllables.  The 
exceptions,  however,  are  so  numerous,  that  this  is  not  to  be 
regarded  as  a  rule,  but  only  as  a  general  tendency  of  pronun- 
ciation. With  respect  to  verbs  of  two  syllables,  the  tendency 
is  to  place  the  aC"''ent  on  the  second  syllable. 

Principles  of  Accent, — Webster's  Dictionary  la3's  down 
several  principles  which  seem  to  have  been  operative  in  deter- 
mining the  position  of  the  accent  of  words,  and  also  in  chang- 
ing it  from  a  former  or  retaining  it  in  its  present  place. 

First.  Derivative  words  take  for  a  time,  if  not  permanently, 
the  accent  of  the  original  words  from  which  they  are  formed. 
The  same  rule  holds  good  with  words  derived  from  other 
English  words  by  adding  one  or  more  syllables  to  their  begin- 
ning or  end ;  as,  improp'er  from  prop'er,  pleas'antly  from 
pleas'ant,  etc. 

Second.  Ease  of  iitterp.nce  has  some  influence  in  decidinir 
the  place  of  accent.  Thus,  accept'able  was  formerly  pro- 
nounced ac'ceptahle,  uten'sil  was  u'tensiU  dyspep/sy  was  dys'- 
pepsy,  suhal'tern  was  suh'altern,  etc.  This  principle  is  an 
important  one  in  determining  the  place  of  accent,  and  though 
many  will   cling   to   the   older  and  harder  pronunciation  as 


TEACHING   PROXUNCIATION.  143 

marked  m  the  dictiouaries,  the  changes  which  promote  ease 
of  utterance  will  liualh'  prevail. 

Third.  In  words  of  two  syllables  there  is  a  tendency  to 
accent  the  lirst  or  penultimate  syllable  ;  as,  com'mon^  prop'er^ 
dis'cord,  etc.  This  principle,  however,  has  mau}-  exceptions. 
It  meets  with  a  powerful  counteraction  from  the  first  princi- 
ple, it  being  natural  in  derivative  words  to  place  the  accent  on 
the  radical  part  of  the  word  ;  as,  confer' ^  distend',  amuse',  etc. 
There  is  a  constant  struggle  among  the  common  people,  how- 
ever, to  draw  back  the  accent  to  the  first  sellable  ;  and  thej"- 
being  in  the  majority,  are  slowly*  gaining  on  those  who  are  gov- 
erned by  the  first  principle. 

Fourth.  In  words  of  three  or  more  s^-llables,  there  is  a 
strong  tendency  to  accent  the  antepenult,  or  third  sjdlable 
from  the  end;  as  in  el'oquent,  ac'cident,  opportu'nity,  etc. 
This  tendency  is  also  counteracted  by  that  of  derivation, 
which  tends  to  arra}^  scholars  against  the  mass  of  the  people, 
man}'  scholars  saying  cont em' plate,  demon' strate ,  etc.,  while 
popular  usage  is  con' template,  dem'onstrate, etc. 

There  are  several  other  principles  which  influence  the  place 
of  the  accent.  Thus,  we  accent  a  word  of  two  S3-llables  when 
used  as  a  noun  or  an  adjective  on  the  first  part ;  and  when 
used  as  a  verb,  on  the  second  part ;  as  con' vert  and  convert'^ 
pro'test  and  protest',  etc.  For  a  fuller  discussion  of  this  sub- 
ject, see  Webster's  Dictionary,  from  which  these  facts  and 
principles  are  drawn. 

Method  of  Teaching. — We  teach  the  correct  accent  of 
words  by  Imitation  and  Correcting  Errors. 

Imitation. — The  teacher  should  be  careful  to  place  the 
accent  correctly  in  speaking  his  words,  that  his  pupils  may 
have  correct  models  for  imitation.  If  the  teacher  continually 
says  i'dea  and  in'quiry,  his  pupils  will  naturally  make  the 
same  mistakes.  Every  teacher  should  make  it  a  special  aim 
to  pronounce  his  words  correctly.  He  should  make  the  dic- 
tionary a  constant  study,  and  also  lead  his  pupils  to  acquire 


144  METHODS   OF   TEACHING. 

tlie  habit  of  consulting  the  dictionary  to  find  out  the  correct 
pronunciation  of  words. 

Errors  of  Accent. — One  of  the  most  common  errors  in  the 
pronunciation  of  words,  is  that  of  misplacing  the  accent. 
Comparative!}'  few  persons,  for  example,  pronounce  idea  with 
the  accent  on  the  second  s^'llable,  or  complex  and  construe 
with  the  accent  upon  the  first  syllable. 

There  is  a  strong  tendency  in  this  country,  among  the 
common  people,  to  give  a  marked  secondary  accent  on  certain 
words,  which  properh^  have  but  one  accent;  as,  difficul'ty, 
cir'cumstan'ces,  in'terest'ing,  etc.  Another  custom,  even 
more  vulgar,  consists  in  placing,  in  words  haA'ing  an  unac- 
cented initial  s^dlable  followed  by  an  accented  one,  a  nearly 
equal  stress  of  voice  on  both ;  as  in  ex'act'ly,  gi'gan'tic, 
i'tal'ic,  po'lit'ical,  etc.  Dickens,  ridiculing  it  in  Martin 
Ghuzzlewit,  makes  one  of  his  characters  sa}"-,  "  Perhaps  there 
ain't  no  such  lo'ca'tion  in  the  ter'rito'ry  of  the  great  U'ni'ted 
States."  The  English,  however,  often  go  to  the  opposite 
extreme,  and  slur  over  the  unaccented  syllables  so  as  to  rob 
them  of  ^le  true  force  which  belongs  to  them. 

The  attention  of  pupils  should  be  called  to  such  mistakes, 
and  pains  should  be  taken  to  have  them  corrected.  Pupils 
should  be  required  to  keep  a  list  of  the  words  which  they  mis- 
pronounce, and  should  be  exercised  on  it  frequently  to  see 
that  they  are  correcting  their  mistakes.  It  requires  constant 
care  and  much  practice  to  change  from  an  incorrect  to  the 
correct  pronunciation  of  a  word. 

Teachers  should  also  make  out  such  a  list  and  drill  them- 
selves daily  on  all  words  which  they  find  they  have  been  mis- 
pronouncing. Many  of  them  will  be  surprised  at  the  extent 
of  the  list,  and  at  the  difficulty  of  the  task  of  correcting  their 
errors.  It  will  sometimes  take  months  and  even  years  to  cor- 
rect some  old  habit  which  has  become  fixed  by  years  of  incor- 
rect practice. 

The  following  is  a  brief  lisi  of  quite  common  words  which 


TEACHIXG    PRONUNCIATION. 


145 


are  frequently  mispronounced.  Let  the  pupil  and  3'oung 
teacher  examine  this  list  and  correct  any  of  their  mispronun- 
ciations, and  use  it  as  the  nucleus  of  other  words  which  ihej' 
find  the}'  have  been  mispronouncing: 


ere, 

often, 

area, 

inquiry, 

Asia, 

ne'er, 

soften, 

vicar. 

vagary. 

Sinai, 

food. 

extol, 

visor. 

equation. 

Alpheus, 

root, 

route, 

gratis, . 

museum, 

gopher, 

dost. 

again. 

complex. 

lyceum. 

Arabic, 

doth, 

recet^s. 

compound. 

interesting, 

Philippi, 

bade. 

dej)ot, 

coiLstrue, 

illustrate, 

Phenice, 

truths, 

carry, 

extant. 

contrary. 

Delilah, 

shew, 

leisure, 

gallows. 

opponent. 

Gennesaret, 

iron, 

exhaust, 

cortege, 

disputant. 

Caucasian, 

idea, 

apostle, 

abdomen, 

vehement. 

Aristobulus, 

error, 

epistle. 

court  e«y. 

nominative, 

Sardanaijalus. 

Recitations,  now  and  then,  sa}'  as  often  as  once  a  week,  in 
the  pronunciation  of  words,  will  be  of  great  benefit  to  pupils. 
There  is  no  reason  why  we  should  not  have  "  Pronunciation 
Mat  jhes,"  as  well  as  "  Spelling  Matches,"  in  our  schools ;  and 
the  teaclier  who  introduces  them  will  find  them  of  great  value. 

Prouoiinciitff  Match.  —  In  a  Pronouncing  Match,  the 
teacher  will  spell  the  words  orally  or  write  them  upon  the 
blackboard,  and  assign  them  to  the  pupils  in  regular  order,  as 
in  the  spelling  match,  the  pupils  "trapping"  or  "going  out," 
as  may  be  preferred.  The  following  method  is  suggested  by 
Mr.  Woodruff : — Make  out  three  lists  of  words,  and  mark  them 
A,  B,  and  C.  Give  the  list  marked  A  to  the  class,  and  when 
all  are  "pronounced  out" but  one,  betakes  his  seat  as  entitled 
to  a  premium.  Call  the  remainder  up  again  and  do  the  same 
with  list  B,  and  then  again  with  list  C,  thus  selecting  two 
others  entitled  to  a  premium.  Then  call  up  these  three 
"  premium  pronouncers,"  and  assign  them  words,  the  last 
down  receiving  the  first  prize,  the  second  down  the  second 
prize,  etc. 
7 


CHAPTER    V. 

TEACHING    ORTHOGRAPHY. 

OKTTTOGKAPTTY  is  the  art  of  expressing  the  elements  of 
unrds.  'riii'st'  fli'inents  may  be  expressed  either  orally  or 
in  writintr.  Wlu'n  expressed  orall}',  the  names  of  the  charac- 
ters may  l)e  given,  or  the  sounds  whicli  the}'  represent;  the 
former  is  the  common  oral  spelling;  the  latter  is  called  pho- 
netic spelling.  Words  ma}'  also  be  spelled  either  upon  hear- 
ing them  pronounced,  or  upon  merely  conceiving  them. 

The  term  Orlfiogrnph;/  is  from  ortJios,  right,  and  grapho^  1 
write,  meaning  literally,  to  write  right.  In  its  primary 
meaning  it  thus  refers  to  written  spelling,  and  this  was  its 
original  use.  Oral  spelling  is  a  secondary  and  derivative  idea 
and  practice.  In  its  true  sense,  orthography'  is  the  represent- 
ation of  spoken  language  by  visible  signs.  It  had  its  origin 
in  picture-writing,  and  has  gradually  |)assed  down  through 
the  verl)al  and  syllabic  stages  to  the  alphabetic  system,  our 
present  letters  being  abbreviations  and  modifications  of  pic- 
tures. 

T,   The  Nature  of  Orthography. 

Itnportfuice The  importance  of   orthography  has  been 

sometimes  over-estimated  and  sometimes  under-estimated. 
Some  teachers  have  made  it  a  hobby  in  the  schools,  and  others 
have  treated  it  with  neglect  and  even  with  contempt.  Its  true 
value  may  be  stated  in  a  single  sentence :  there  is  no  great 
credit  in  being  a  good  speller,  but  there  is  gi-eat  discredit  in 
being  a  poor  one.  Dr.  Currie  gives  a  similar  estimate  when 
he  savs,  ''  The  possession  procures  no  credit,  but  the  want 
entails  disgrace."     Prof.  March  sa3's,  "  Stress  is  laid  on  it  aa 

(140) 


NATURE    OF    ORTHOGKAPIIY.  147 

the  sign  of  a  thoroughly  educated  person  out  of  all  proportion 
to  its  real  value."  Still,  correct  spelling  can  not  but  be 
regarded  as  an  indication  of  a  cultivated  and  scholarly  mind. 

The  attention  it  has  received  during  the  past  fifty  years  has 
varied.  Manj^  years  ago,  when  there  were  few  studies  in 
the  public  schools,  orthography  occupied  a  large  share  of  the 
teacher's  attention.  The  old  "  spelling  schools"  have  become 
historic.  Subsequently,  when  geography,  grammar,  mental 
arithmetic,  etc.,  were  introduced,  orthography  was  eclipsed  in 
interest,  and  was  greatly  neglected.  After  a  while,  it  was  seen 
that  boys  and  girls  w^re  coming  out  of  the  public  schools 
poorer  spellers  than  cheir  parents,  and  a  reaction  took  place 
in  favor  of  ortnography.  To-day  it  is  receiving  its  just  share 
of  attention. 

Difficulty -English  orthography  is  exceedingly  difficult : 

it  is  probably  more  difficult  than  that  of  any  other  modern 
language.  American  children  spend  three  years  in  learaing 
to  spell  a  little,  while  German  children  get  further  in  a 
twelvemonth.  In  the  civil  examinations  in  England,  out  of 
1972  failures,  1866  candidates  failed  in  spelling;  audit  is  said 
that  the  documents  prepared  by  the  prime  ministers  of  Eng- 
land show  that  no  one  of  them  could  have  passed  these  exami- 
nations in  spelling. 

This  difficulty  is  due  to  the  irregularity  of  the  English 
orthography.  This  irregularity  consists  in  the  use  of  silent 
letters,  and  in  the  use  of  ditferent  letters  and  combinations  to 
represent  the  same  sound.  Many  letters  are  pronounced  in 
several  different  ways,  while  the  letters  or  combinations  of 
letters  for  a  single  sound,  in  some  cases  amount  to  scores 
Many  words  of  no  more  than  two  syllables  may  be  spelled  in 
several  thousand  different  ways,  by  the  use  of  combinations 
actually  employed  in  other  words  in  the  language.  The  word 
scissors,  it  is  computed  by  Ellis,  may  be  thus  written  in 
nearly  6000  different  ways.  Indeed,  it  may  be  truly  said  that 
we  possess  the  worst  alphabetic  spelling  in  the  world.     Eng- 


148  METHODS   OF   TEACHING. 

lish  ortliograph}'  is  "the  opprobrium  of  English  scholarship;" 
it  is  the  greatest  hindrance  to  education  and  to  the  spread  of 
our  language. 

Orif/in. — The  irregularity  of  our  orthography  is  accounted 
fc'  by  its  histor}".  The  Anglo-Saxon  was  first  reduced  to 
writing  by  the  Roman  missionaries  who  converted  the  people 
to  Christianity.  They  used  the  Roman  letters,  in  nearly  their 
Roman  value,  and  added  new  characters  for  the  sound  of  a  in 
fat,  th  in  their  ((//(),  th  in  thine,  and  w.  The  Norman  Conquest 
produced  chaos  in  English  spelling.  The  Normans  and  Saxons 
could  nt)t  pronounce  each  other's  words  correctly;  and  in  trying 
to  spell  them,  confusion  and  uncertainty  became  inevitable. 

Carelessness  in  authors  and  copyists  also  contributed  to  this 
irregularity.  Before  the  time  of  printing,  manuscripts  show  that 
the  wildest  license  prevailed  in  spelling  words.  Even  proper 
names  are  found  recorded  in  a  great  multitude  of  forms,  several 
variations  boi'ig  sometimes  found  in  the  same  manuscript.  Dis- 
raeli says  that  "Leicester  has  subscribed  his  own  name  eight 
different  ways,"  and  that  "the  name  Villers  is  spelled  fourteen 
different  ways  in  the  deeds  of  that  family."  Lower  states  that 
the  family  of  Mainivaring  has  131  variations  of  that  single  name, 
all  drawn  from  authorized  documents. 

There  were  a  few  writers,  however,  in  those  early  days,  who  were 
attentive  to  the  proper  form  of  words.  The  spelling  of  the  Onnu- 
him,  which  was  written  in  the  13th  century,  though  strange  and 
cumbrous,  is  remarkable  for  its  regularity;  and  the  author  urges 
his  copyists  to  follow  his  orthography  with  the  utmost  exactness. 
Chaucer,  also,  more  than  a  century  later,  carefully  revised  and 
corrected  his  own  works;  and  he  enjoined  upon  his  scribe  to 
"write  more  trew"  that  which  was  intrusted  to  him,  saying  that 
he  was  obliged  "it  to  correct  and  eke  to  rubbe  and  scrape,"  be- 
cause of  the  negligence  and  haste  with  which  it  had  been  copied. 
Even  as  late  as  the  time  of  Shakespeare,  orthography  was  very 
unsettled,  for  the  name  of  the  great  poet  was  written  more  than 
thirty  different  ways. 


TEACHING   ORTHOGRAPHY,  149 

The  invention  of  printing  contributed  largely  to  fix  the  orthog- 
raphy of  words.  For  a  long  time,  however,  it  did  but  little  to 
give  uniformity  to  spelling.  There  being  no  standard,  printers 
added  or  omitted  letters,  as  the  length  of  the  line  or  convenience 
of  spacing  required.  The  same  word  was  often  printed  in  several 
different  ways  on  the  same  page.  At  length  the  attention  of 
scholars  was  directed  to  the  subject,  and  efforts  were  made  to  im- 
prove and  settle  English  orthography. 

Dr.  Johnson's  celebrated  Dictionary,  published  in  1755,  was 
the  first  recognized  standard  of  orthography;  and  it  has  con- 
tributed more  than  any  work,  either  before  or  since,  to  fix  our 
method  of  spelling.  It  settled  usage  definitely  in  favor  of 
some  one  of  the  numerous  forms  in  which  words  were  written, 
and  thus  removed  the  cause  of  confusion.  He  introduced 
changes  to  restore  the  ancient  orthography  or  to  remove  some 
anomaly,  some  of  which  were  not  adopted  by  subsequent 
writers.  Among  these  were  the  restoration  of  k  to  many 
words  that  had  been  written  without  it ;  as,  viusick,  rhetorick, 
etc.,  and  the  insertion  of  u  in  many  words  ending  with  or-,  as 
honour,  ancestour,  etc.  This  latter  method  is  still  used  by 
many  English  writers. 

In  1828,  Noah  Webster  published  his  great  Dictionary  of 
the  English  language,  in  wliich  he  made  many  changes  in 
orthography.  These  changes  were  of  two  kinds:  first,  to 
make  the  words  correspond,  as  far  as  practicable,  with  their 
primitive  forms,  so  as  to  reveal  their  etymological  affinities ; 
second,  to  reduce  as  much  as  possible  the  number  of  anomalies 
and  special  cases.  Of  the  former  class,  many  were  restored 
by  Dr.  Webster  in  the  second  edition  of  his  work,  published 
in  1840;  and  others  were  restored  in  subsequent  editions. 
Many  alterations  of  the  second  class  have  been  received  with 
favor  and  adopted  by  a  large  number  of  writers  in  the  United 
States,  and  by  some  English  authors. 

Phonetic  Systems. — The  irregularity  of  English  orthogra- 
phy has  led  to  many  attempts  for  the  adoption  of  a  phonetic  sy  s- 


150  METHODS   OF    TEACHING. 

tern  of  spelling.  The  first  of  these  was  made  by  Sir  Thomas 
Smith  (1568),  Secretary  of  State  to  Queen  Elizabeth.  He 
was  followed  by  John  Hart  (1569),  Chester  herald,  by  William 
Bullokar  (1580),  by  Dr.  William  Gill  (1619),  Master  of  St. 
Paul's  School,  London,  and  in  1633  by  Charles  Butler,  who 
printed  a  book  in  which  his  new  method  was  employed.  In  the 
time  of  Charles  I.,  many  changes  were  introduced,  and  it  was 
very  common,  even  among  eminent  scholars,  to  spell  words  as 
they  were  pronounced,  omitting  such  letters  as  were  deemed 
superfluous.  These  attempts,  however,  being  made  upon  no  set- 
tled or  uniform  principles,  had  little  or  no  permanent  effect  upon 
the  language. 

The  attempt  to  reform  our  orthography  by  employing  an  al- 
phabet in  which  each  sign  shall  stand  for  one  and  only  one 
sound,  has  been  made  in  modern  times.  Dr.  Franklin  invented 
such  a  system,  though  he  never  brought  it  to  perfection,  and 
scarcely  used  it  except  in  a  brief  correspondence  with  a  friend. 
The  most  important  systems  recently  presented  are  those  of  A.  J. 
Ellis,  I.  Pittman,  E.  Jones,  and  A.  M.  Bell.  Mr.  Bell  has  in- 
vented a  set  of  characters  which  indicate  by  their  form  the  po- 
sition of  the  organs  of  speech,  being  thus  a  system  of  "visible 
speech."  Scholars  have  begun  to  use  it  in  scientific  treatises; 
but  it  can  hardly  meet  with  general  adoption. 

Reform  in  SpeUhi<j. — There  seems  to  be  a  growing  opinion 
in  favor  of  a  reform  in  our  orthography.  The  leading  philolo- 
gists of  this  country  and  England  are  becoming  strong  advocates 
of  it.  Among  these  we  may  mention  the  names  of  March,  Whit- 
ney, and  Haldeman,  of  America,  and  Max  Midler,  Ellis,  Jones, 
etc.,  of  England.  Many  of  the  philological  and  teachers'  asso- 
ciations of  both  countries,  and  also  some  state  legislatures,  have 
appointed  committees  to  consider  the  subject. 

The  disadvantages  of  our  present  system  make  a  change  a 
necessity.  Our  system  of  spelling  is  one  of  the  greatest  hin- 
drances to  the  education  of  our  people.  Children  require 
years  of  study  in  order  to  learn  to  spell  and  pronounce  written 


TEACHING   ORTHOGRAPHY.  151 

words,  which  couhl  be  learned,  if  we  had  a  phonetic  system, 
in  ;i  few  weeks  or  months.  Besides  this,  millions  of  dollars 
are  wasted  everj-  ^-ear  in  printing  silent  letters  and  senseless 
combinations  to  express  simple  sounds. 

That  some  change  will  be  made,  seems  probable,  but  what 
form  it  will  assume,  it  is  ditlicult  to  tell.  The  essential  prin- 
ciple of  a  radical  change  is  that  each  sound  shall  be  repre- 
sented by  a  single  character,  and  that  words  shall  be  spelled 
as  pronounced.  We  should  therefore  take  the  present  letters, 
using  each  for  its  most  common  sound,  invent  some  fourteen 
or  sixteen  new  cliaracters  for  the  remaining  sounds,  and  then 
spell  words  as  the}'  are  pronounced,  using  no  more  characters 
in  a  word  than  are  sounded. 

The  objections  to  this,  liowever,  are  man\'  and  serious. 
What  shall  be  done  with  tiie  vast  libraries  of  books  already 
printed,  which  will  become  sealed  volumes  to  those  taught  by 
the  new  method?  How  sii:dl  we  get  the  people  to  learn  the 
new  method,  or  to  allow  it  to  be  introduced  into  the  schools 
of  the  country'?  Indeed,  the  objections  are  so  great  as  to  be 
absolutely  insuperable.  It  may  therefore  be  positively  as- 
sumed that  no  phonetic  system  will  be  adopted;  and  in  what 
form  a  reformation  will  come  it  is  at  present  impossible  to 
[predict. 

TI.   Methods  of  Teaching  Orthography. 

There  are  two  methods  of  teaching  orthography,  which  may 
be  distinguished  as  the  Oral  and  the  Written  Method.  The 
Oral  Method  depends  upon  the  sense  of  hearing,  and  the 
Written  Method  ujion  the  sense  of  sight.  They  have  also 
been  distinguished  as  the  Auricular  (a«ri,s",  the  ear)  and  the 
Oi'ulai  (oculus,  the  eye);  but  the  terms  Oral  and  Written 
seem  to  have  been  more  generally  adopted  b}'  the  profession. 

The  Oraf  Mcf It od.— The  Oral  Method  is  that  which 
teaches  orthograjihy  by  naming  the  letters  of  words  ;  it  is 
based  upoii  the  principle  of  fixing  in  the  memory  the  letters 


152  METHODS   OF   TEACHING. 

of  words  in  their  order  through  the  sense  of  hearing.  It  con- 
sists in  memorizing  the  sound-order  of  letters,  with  the 
expectation  that  the  association  of  the  names  will  become 
fixed  in  the  memory-  in  their  proper  order  like  the  words  of  a 
quotation. 

The  Oral  Method  possesses  several  advantages.  It  teaches 
pupils  to  pronounce  words,  which  the  "Written  Method  does 
not.  It  also  teaches  the  correct  syllabication  of  words,  which 
is  not  done  by  the  ordinary  Written  Method.  It  also  admits 
of  several  interesting  methods  of  competitive  recitation.  The 
spelling-match  is  essentially  an  oral  exercise :  a  written  spell- 
ing-match is  a  dull  thing,  compared  with  the  old-fashioned 
oral  spelling-matches. 

There  arc  also  several  disadvantages  in  the  Oral  Method  as 
compared  with  the  Written  Method.  First,  pupils  taught  to 
spell  orally  will  not  usually  spell  correctly  when  they  are 
■writing.  It  is  frequently  noticed  that  pupils  will  spell  without 
mistake,  when  pronounced  to  them,  the  words  which  they 
have  misspelled  in  a  letter  or  a  composition.  This  objec- 
tion becomes  more  serious  when  we  remember  that  the  princi- 
pal value  of  spelling  is  the  ability  to  write  words  correctly. 
There  is  no  particular  value  in  spelling  words  orally.  An- 
other objection  is  that  each  pupil  of  a  class  cannot  spell  as 
many  words  of  the  lesson  as  by  the  Written  Method. 

The  Oral  Method,  notwithstanding  these  objections,  is  the 
one  which  has  been  almost  exclusively  used  for  centuries.  It 
is  within  a  comparatively  recent  period  that  the  Written 
Method  has  been  introduced  into  our  schools.  Our  fathers 
were  all  taught  by  the  Oral  Method,  and  even  the  majority  of 
the  teachers  of  the  present  day  were  trained  by  it. 

Ths  Written  Method The  Written  Method  is  that  which 

teaches  orthography  by  writing  the  letters  of  words.  It  is 
based  upon  the  principle  of  fixing  the  orthographical  struc- 
ture of  words  upon  the  memory  through  the  sense  of  sight 
It  assumes  that  the  word  is  presented  to  the  mind  as  a  pic- 


TEACHING    ORTHOGRAPHY.  153 

turc,  in    which   the   elements   are   distinct!}^   perceived   and 
remembered  in  their  order. 

There  are  man}-  advantages  of  the  Written  Method  as  com- 
pared with  the  Oral  Method.  First,  we  learn  to  spell  more 
readily  by  sight  than  b}^  sound.  That  which  we  see  makes  a 
deeper  impression  on  the  mind  than  that  which  we  hear.  The 
old  adage  that  "  Seeing  is  believing,"  expresses  this  fact.  In 
proof  of  this  principle,  it  is  said  that  the  deaf,  w^ho  must  use 
the  Written  Method,  learn  to  spell  more  readilj^  than  the 
blind.  It  is  also  a  common  experience,  that  wdien,  in  writing 
a  letter,  we  are  in  doubt  about  the  orthography  of  a  word,  we 
write  it  on  a  piece  of  paper  to  see  how  it  looks.  Good  spell- 
ers tell  us  that  in  spelling  orally  the^-  usually  picture  words 
in  their  minds,  and  name  the  letters  accordingly. 

A  second  advantage  of  the  Written  Method  is,  that  a  pupil 
taught  by  this  method  will  spell  correctly  when  he  writes, 
which  is  the  principal  point  aimed  at  in  the  stud}-  of  orthog- 
raphy. Experieivce  has  shown  that  a  pupil  may  be  skilled  in 
oral  spelling,  and  make  many  mistakes  in  orthography  in  his 
letters  and  compositions. 

A  third  advantage  is  that  b}^  the  Written  Method  the  pupil 
will  spell  all  the  words  in  the  lesson,  while  by  the  Oral  Method 
he  spells  onl}'  part  of  the  words.  The  Written  Method  thus 
gives  a  more  thorough  drill  in  orthography  during  the  recita- 
tion than  the  Oral  Method.  It  also  affords  a  better  test  of 
the  comparative  skill  of  the  members  of  the  class,  since  all 
spell  the  same  words. 

A  fourth  advantage  is  that  it  gives  the  pupil  an  opportunit}' 
to  review  the  misspelled  words.  This  is  one  of  the  most  im- 
portant points  of  a  lesson  in  orthography.  In  any  ordinary 
8})elling-lesson,  the  pupil  can  spell  one-half  of  the  words  before 
looking  at  tLem  ;  it  is  the  hard  words  which  he  is  liable  to  miss, 
that  it  is  most  important  for  him  to  study.  If  he  misses 
these  words  and  is  not  drilled  upon  them  till  he  can  spell  them 
correctly,  he  receives  no  advantage  from  the  lesson      By  the 


154  METHODS   OF    TEACHING. 

Oral  Method,  the  teacher  cannot  tell  what  words  each  member 
of  the  class  is  unable  to  spell  ;  and  it  would  be  very  inconve- 
nient for  him  to  keep  a  list  of  the  words  that  are  missed  in 
order  that  they  may  be  reviewed  b^'  the  pupil. 

Ajiother  advantage  is  that  it  keeps  all  the  pupils  emplo3-ed 
during  the  recitation  and  holds  the  attention  of  all.  A  por- 
tion of  the  class  cannot  be  inattentive  while  the  others  are 
spelling,  as  is  often  the  case  in  the  Oral  Method.  It  should 
also  be  remarked  that  the  pupil  who  learns  to  spell  by  the 
Oral  Method  of  recitation  is  actuall}'  learning  orthograph}'  by 
seeing  the  words  as  he  studies  them,  and  that  he  depends  in 
spelling  on  his  memory  of  the  form  of  the  word,  rather  than 
upon  the  recollection  of  the  order  of  the  names  of  the  letters. 

Having  considered  the  character  of  the  two  methods  of 
teaching  orthograpli^-,  we  will  now  describe  the  manner  of 
conducting  recitations  according  to  each. 

III.  Written  Method  of  Teaching  Orthography. 

A  written  recitation  in  orthography  may  be  conducted  by 
using  Slates,  or  the  Blackboard,  or  Blank  Books.  The  meth- 
ods with  Blackboards  and  Blank  Books  are  now  the  more 
generally  emi)loyed.     We  shall  describe  each. 

Bhickhoaid  Method. — In  an  exercise  upon  the  Black- 
board, the  first  thing  is  the  preparation  of  the  board.  The 
pupils  should  erase  all  the  work  upon  the  part  of  the  board  to 
be  used,  divide  it  into  equal  si)aees  by  vertical  lines,  and  each 
pupil  write  his  name  at  or  near  the  upper  part  of  the  space  he 
IS  to  use.  The  erasing  and  spacing  may  also  be  done  by  a 
committee,  if  the  teacher  prefers. 

Writintj  the  Words. — The  next  step  is  the  writing  of  the 
words.  The  words  should  be  written  in  vertical  columns 
rather  than  in  horizontal  lines.  Ordinary  words  should 
begin  with  small  letters,  and  proper  names  with  capitals. 
They  should  not  be  followed  with  any  mark  of  punctuation,  as 


TEACHING   ORTHOGRAPHY.  155 

no  grammatical  relations  are  to  be  expressed.  Care  should,^ 
be  taken  that  the  writing  be  neat  and  legible.  The  i's  should 
be  dotted  and  the  /'*;  crossed,  and  care  taken  b}'  the  pupil  to 
prevent  any  doubt  as  to  the  manner  in  which  he  intended  to 
spell  the  word.  The  following  couplet,  familiar  to  many  of 
the  teachers  of  our  jjublic  schools,  presents  a  good  practical 
rule : 

"Dot  your  Cs  and  cross  your  fs, 
Close  your  o's  and  open  your  ^s." 

Pupils  may  sometimes  be  required  to  divide  words  into  sa'I- 
lables  bj-  means  of  a  hvphen.  This  will  teach  them  the  proper 
syllabication  of  words,  a  knowledge  which  is  often  of  use  to 
them  in  writing.  A  dash  should  not  be  used  for  this  division ; 
too  great  a  distance  between  the  s^'llables  destroj'S  the  natural 
appearance  of  the  words.  An  advantage  peculiar  to  the  oral 
metliod  is  thus  secured  in  the  written  method  of  orthography. 
The  teacher  may  also  occasionalh'  require  them  to  mark  the 
accented  syllables  of  words. 

Instead  of  each  pupil  writing  the  same  word,  the  class  may 
be  divided  into  two  sections  standing  alternatelj^  by  counting 
one,  tivo,  one,  hvo,  et(?r,  the  ones  taking  one  word,  and  the  tivos 
the  following  word.  Or  the  sections  may  be  formed  by  num- 
bering 07ie,  two,  three,  four,  etc.,  the  odd  numbers  writing  one 
word  and  the  even  numBers  writing  the  next  word.  There 
are  two  advantages  in  this:  first,  while  one  section  is  writing, 
the  teacher  can  be  pronouncing  a  word  for  the  following  sec- 
tion; second,  it  removes  the  temptation  of  copying  a  word 
from  a  neighbor,  as  each  pupil  stands  between  those  who  are 
writing  a  different  list  from  his  own. 

Corrections. — After  the  words  are  written,  the  next  thins: 
is  the  correction  of  the  words  that  have  been  misspelled.  In 
making  the  corrections,  the  teacher  spells  the  words,  and 
the  pupils  notice  whether  they  have  written  them  correctly, 
marking  the  misspelled  words.  These  maj^be  marked  by  the 
figures,  1,  2,  3,  etc.,  or  by  drawing  a  line  under  the  word,  or 


156  METHODS   OF   TEACHING. 

by  placing  a  cross,  x  ,  after  each  misspelled  word.     The  latter 
'method  is  preferred.     After  the  misspelled  words  have  been 
marked,  they  should  be  counted,  and  the  number  of  them 
written  above  or  below  the  columns. 

The  corrections  should  be  made  by  the  pupils  rather  than 
by  the  teacher.  Each  pupil  may  correct  his  own  mistakes;  or, 
at  a  signal,  they  may  all  change  places  and  each  pupil  correct 
the  work  of  another.  Many  teachers  prefer  the  latter  method, 
since  it  removes  the  temptation  to  deceive.  I  should  lie- 
quentl}^,  however,  use  the  former  method,  creating  a  moral 
sentiment  in  the  class  that  will  protect  the  pupils  from  deceit 
and  thus  strengthen  their  moral  natures. 

3Iisspelled  Words. — The  next  step  is  to  take  a  list  of  the 
misspelled  words.  These  words  should  be  written  in  a  blank 
book  prepared  for  this  purpose.  The  pupils  should  review 
these  words  as  often  as  once  a  week,  and  there  should  be  a 
final  review  of  them  at  the  close  of  the  session. 

Use  of  B/dHk  Hooks. — Blank  books,  prepared  for  the  pur- 
pose, may  be  used  for  writing  the  words  instead  of  the  black- 
board. The  words  should  be  written  neatly  with  pen  and 
ink.  The  method  of  writing  is  the  same  as  that  already  de- 
scribed in  using  the  blackboard.  The  corrections  may  be  made 
by  the  pupils,  but  it  is  preferred  that  the  books  be  handed  to 
the  teacher,  and  the  corrections  be  made  b^-^  him.  The  pupil 
should  then  write  a  list  of  each  day's  errors  in  the  latter  part 
of  the  book.  It  will  be  well  to  begin  such  a  list  on  the  last 
page  of  the  book,  as  the  pupil  cannot  know  how  much  room 
will  be  required  for  it. 

An  advantage  of  this  method  is  that  a  pei'manent  record  of 
the  spelling  exercises  is  kept.  It  is  also  more  convenient  to 
keep  a  record  of  the  misspelled  words  than  by  the  blackboard 
method.  The  method  is  especially  recommended  for  the  ad- 
vanced classes,  and  also  when  the  classes  are  large. 

Use  of  Slates. — In  using  slates,  the  pupils  write  the  words 
on  their  slates,  as  in  the  former  methods.    Each  pupil  may  then 


TEACHING   ORTHOGRArilY.  157 

correct  his  mistakes  as  the  teacher  spells  the  words,  or,  at  a 
signal,  slates  may  be  exchanged,  and  one  pupil  correct  for 
another.  The  misspelled  words  should  be  copied  in  a  blank 
book  at  the  close  of  the  recitation.  This  method  is  more  con- 
venient for  copying  the  misspelled  words  than  the  blackboard 
method,  though  it  has  the  disadvantage  that  the  teacher  is 
not  able  to  see  the  words  while  the  pupils  are  writing.  It  is 
now  less  used  than  either  of  the  two  previous  methods. 

Dictation  Exercises. — Instead  of  always  writing  words 
abstractly  in  columns,  pupils  should  often  be  required  to  write 
words  as  they  occur  in  sentences.  Such  exercises  may  be  dic- 
tated by  the  teacher,  and  are  called  Dictation  Exercises.  The 
teacher  may  form  sentences  containing  certain  words,  and 
have  pupils  write  as  he  dictates  them ;  or  he  may  give  them 
one  or  more  words,  and  have  them  write  sentences  containing 
the  words.  He  may  also  read  sentences  and  paragraphs  from 
a  book  or  a  newspaper,  and  have  them  written.  Pupils  should 
be  required  to  be  careful  about  the  use  of  capital  letters, punc- 
tuation and  quotation  marks,  etc.  The  corrections  may  be 
made  as  before  explained. 

There  are  many  advantages  in  dictation  exercises.  They 
will  teach  pupils  how  to  spell  words  correctly  as  they  use  them 
m  writing  letters,  etc.  Thev  will  be  found  more  interesting 
to  pupils  than  writing  words  abstractly  in  columns.  They 
will  also  teach  the  pupils  the  meaning  of  such  words  as  they 
may  not  understand,  and  show  how  to  use  them  correctly. 
They  will  atford  pupils  a  practical  exercise  in  composition, 
and  teach  them  the  correct  use  of  capitals,  punctuation 
marks,  etc. 

TV.  The  Oral  Method  of  Teaching  Orthography. 

The  Oral  Method  of  teaching  orthography  is  that  which 
endeavors  to  fix  the  correct  spelling  of  a  word  in  the  memory 
bv  calling  the  names  of  the  letters.  It  should  be  remarked, 
however,  that  in  reality  this  oral  method  is  more  a  form  of 


158  METHODS    OF    TEAC.llXJ. 

recitation  than  of  learning  orthography.  Even  when  the 
pupil  recites  by  this  method,  he  is  learning  by  looking  at  the 
words,  as  he  studies  his  lesson. 

In  describing  the  Oral  Method  of  teaching  orthography, 
there  are  several  special  points  which  require  our  attention. 
The  first  is  the  Position  of  the  Pupil,  the  second  is  the  Assign- 
ment of  the  Words,  the  third  is  the  Method  of  Spelling,  and 
the  fourth  is  Spelling  Matches. 

Position  of  Piipits. — The  jjupils  while  spelling  may  be 
either  seated  or  standing.  If  seated,  the^'  should  be  as  near 
one  another  as  may  be  convenient.  They  should  sit  erect, 
with  their  hands  in  their  laps  or  on  the  desk,  and  their  feet 
on  the  floor.  If  standing,  they  should  be  in  a  straight  line  if 
possible,  their  feet  in  a  proper  position,  their  toes  on  a  line, 
their  hands  hanging  naturall}'  by  their  side,  or  folded  in  front, 
or,  in  the  case  of  ver}'  young  pupils,  behind  their  backs,  to 
keep  them  out  of  mischief;  the  shoulders  should  be  thrown 
slightly  back,  and  the  body  erect  in  a  natural  and  healthful 
position. 

Assif/nment  of  Words — The  words  may  be  assigned  regu- 
larly from  head  to  foot,  or  to  the  members  miscellaneously 
The  latter  is  best  adapted  to  secure  attention;  but  the  formei 
is  necessary  if  the  method  of  "  trapping"  is  used.  The  words 
themselves  should  be  selected  miscellaneously,  and  not  in  the 
order  of  the  book,  to  prevent  pupils'  calculating  and  preparing 
their  own  words.  When  a  word  has  been  spelled  correctly, 
another  word  should  be  assigned ;  when  a  word  is  missed  by 
a  pupil,  the  word  is  to  be  passed  to  the  next  and  continued 
from  one  to  anotlier  until  it  is  spelled  coi'rectly. 

Another  method  of  assiuning  words  is  that  in  which  the 
teacher  does  not  indicate  to  the  pupils  when  a  word  is  mis 
spelled,  but  goes  on  and  assigns  the  next  word  as  if  the  pre- 
vious word  had  been  correctly  spelled.  Every  pupil  is  required 
to  watch  the  spelling  of  each  word,  and  if  the  previous  wor<l 
has  been  misspelled,  he  should  spell  it  correctly  rather  than 


TEACHING    ORi'ilUGlt.Vi'Uy.  159 

the  word  assigned  to  him.  This  is  an  excellent  method  to 
secure  the  attention  of  the  class. 

A  method  somewhat  similar  to  the  preceding  is  for  tlie 
teacher  frequently'  to  assign  the  word  just  spelled,  to  the  next 
pupil,  whether  correctly'  or  incorrecth'  spelled.  This  keeps 
each  pupil  attentive  to  the  spelling  of  every  word,  for  the 
teacher's  '"next"  is  no  indication  that  the  word  is  missjDelled. 
It  keeps  a  class  wide  awake,  requii-es  each  one  to  spell  men- 
tall3'  nearl}^  ever}'  word,  and  gives  a  certainty  of  opinion  and 
decision  with  respect  to  the  orthography  of  a  word. 

Another  method  is  to  allow  the  pupils  to  assign  words  to 
each  other,  beginning  after  the  first  with  the  final  letter  of  the 
word  last  spelled.  This  is  an  excellent  exercise  for  variety, 
and  awakens  a  great  deal  of  interest.  It  also  affords  pupils 
an  exercise  in  thinking  quickly  of  words. 

In  assigning  words,  the  teacher's  rule  should  be,  to  pro- 
nounce the  word  but  once.  If  a  teacher  is  accustomed  to 
pronounce  several  times,  the  pupils  will  become  accustomed  to 
requiring  it;  if  the  rule  is  to  pronounce  but  once,  there  will 
seldom  be  occasion  to  repronounce  a  word,  I  would  depart 
from  this  rule  only  when,  on  account  of  some  noise,  or  for 
other  reasons,  there  was  a  good  excuse  for  a  pupil's  not  un- 
derstanding the  word.  When  a  word  is  missed,  in  passing  it 
to  the  next  pupil,  it  should  not  be  repronounced  ;  each  pupil 
should  understand  every  word  assigned.  Of  course,  with  very 
5'oung  pupils,  a  little  allowance  must  be  made  for  circum- 
stances which  may  distract  the  attention. 

Again,  the  teacher  should  not  depart  from  the  correct  pro- 
nunciation of  a  word  to  aid  a  pupil  in  spelling  it.  Thus  he 
should  not  pronounce  "  sep-a-rate,"  or  "  ed-z'-ble,"  etc.,  thus  in- 
dicating the  spelling  of  the  word  by  a  mispronunciation  of  it. 
This  is  sometimes  done  through  sympathy,  to  keep  a  pupil 
from  missing,  but  it  is  nevertheless  wrong.  If  the  pupil  can- 
not spell  the  word  without  this  help,  he  simply  does  not  know 
how  to  spell  the  word  and  should  fail  on  it. 


160  METHODS   OF    TEACHING. 

Spelling  the  Words. — When  the  word  is  assigned,  the 
pupil's  first  duty  is  to  pronounce  the  word.  The  object  of 
tliis  is  to  see  if  the  word  to  be  spelled  is  distinctly  understood. 
The  next  step  is  to  name  the  letters  of  the  word  in  their  order, 
pronouncing  the  syllables,  and  pronouncing  the  entii-e  word  at 
its  close.  Pupils  may  also  spell  by  syllables,  or  even  by  letters, 
that  is,  each  pupil  spelling  one  syllable  or  naming  one  letter 
in  a  word.     This  latter  method  is  only  for  variety',  however. 

As  a  rule,  I  would  rei^uire  pupils  to  pronounce  the  syllables 
of  words  as  they  spell  them.  When  so  required,  they  should 
pronounce  the  S3'llable  even  when  it  consists  of  but  one  letter, 
as  in  the  word  lin-i-ment,  for  often  the  name  of  the  letter  is 
not  its  sound  in  pronouncing  the  word.  I  would  require  also 
that  the  previous  part  of  the  word  be  repeated  in  connection 
with  each  new  syllable  ;  as,  l-i-n,  lin,  i,  e,  lini,  m-e-n-t,  merit. 
liniment.  With  the  more  advanced  pupils  and  with  long 
words,  it  may  be  sufficient  merely  to  pronounce  each  syllable 
as  it  is  spelled,  pi-onouncing  the  word  at  its  close  ;  thus,  l-i-n, 
lin,  i,  e,  m-e-n-t,  meat^  liniment.  With  the  most  advanced 
pupils,  it  will  be  sufficient,  a  portion  of  the  time,  to  have  them 
simply  name  the  letters  in  their  order,  indicating  the  separa- 
tion of  the  syllables  by  pausing  between  them  ;  as,  l-i-n-i- 
m-e-n-t,  liniment. 

The  pupils  should  speak  in  a  natural  tone  of  voice.  Do  not 
allow  them  to  pitch  their  voices  upon  a  high  key,  and  shout 
or  drawl  out  the  sounds.  The  "  spelling  tone,"  heard  in  many 
schools,  is  very  objectionable.  Neither  should  a  pupil  be  al- 
lowed to  mumble  his  words.  Each  element  and  syllable  should 
be  enunciated  in  a  full,  natural,  and  distinct  tone  of  voice. 

Pupils  should  also  be  required  to  spell  phonetically,  that  is, 
by  giving  the  elementary  sounds  which  compose  words. 
Such  an  exercise  belongs  more  particularly  to  pronunciation, 
and  comes  under  the  head  of  jjhonic  analysis;  but  it  will  be 
convenient  to  have  it  also  in  the  spelling  classes. 

The  Spelling  Match. — One  of  the  most  interesting  and 


TEACHING    ORTHOGKAPHr,  161 

instructive  exercises  of  the  oral  method  is  the  spelling  match. 
Its  competitive  principle  is  a  stimulus  for  preparation;  and  it 
carries  with  it  all  the  excitement  of  contest  and  satisfaction  of 
triumph  that  is  felt  in  a  game  of  base-ball  or  other  contest  of 
skill.     We  shall  describe  it  somewhat  in  detail. 

The  sides  are  usually  chosen  by  two  persons  of  about  equal 
spelling  ability,  appointed  by  the  teacher  or  selected  by  the 
class.  These  "leaders"  or  "captains"  select  the  members  of 
their  sides,  by  alternate  choice  until  all  who  are  to  participate 
are  chosen.  There  are  several  methods  of  conductin*'-  the 
exercise,  which  we  shall  attempt  to  distinguish  by  character- 
istic names,  and  to  describe. 

Spelling  Down. — The  usual  method  is  for  the  opposing 
parties  to  ^tand  on  opposite  sides  of  the  room,  words  being 
assigned  to  each  side  alternately.  When  a  word  is  missed  on 
one  side,  t'le  person  missing  it  takes  his  seat,  and  the  word  is 
l)assed  to  the  opposite  side,  or  dropped,  etc.  The  contest  is 
decided  by  one  side  being  "  spelled  down  ; "  or  b^-  comparing 
the  uumbei'  left  standing  at  the  close  of  the  match. 

Saving  and  Out. — A  variation  of  this  method,  known 
among  pupils  as  "saving  and  out,"  is  that  in  which,  when  a 
word  is  missed  on  both  sides,  the  side  which  at  last  spells  it, 
saves  those  of  its  own  number  who  have  missed  it  from  aroinsr 
out.  Those  on  the  opposite  side,  however,  who  have  missed 
the  word,  take  their  seats. 

Passing  Over. — Another  method  is  that  in  which  when  a 
word  is  missed  on  one  side  and  spelled  on  the  other,  those 
who  missed  it  pass  to  the  side  which  spelled  it.  A  variation 
of  this  method  is  to  give  the  leader  of  the  side  a  choice  of  one 
of  the  opposite  party.  This  method  is  objectionable  on  ac- 
count of  the  noise  and  confusion  of  passing  over,  and  also  for 
other  reasons. 

Climbers. — Another  method  is  to  send  the  best  speller  of 
each  side  to  the  foot  of  the  opposite  side,  and  then  assign 
words  from  head  to  foot  of  each  side,  the  "cKmber"  moving 


162  METHODS    OF   TEACHING. 

towards  head  for  every  missed  word  that  he  spells.  The  side 
whose  climber  reaches  head  first,  or  at  the  end  of  the  lesson  is 
the  nearest  head,  wins  the  victor}'. 

Cfiainpions. — Another  method  is  for  each  side  to  select 
cliampions  who  step  out  from  tlieir  ranks,  and  like  the  ancient 
champions  before  a  battle,  engage  in  a  personal  contest,  the 
teacher  assigning  words  alternately  to  them  until  one  of  theni 
misses  and  falls.  The  side  spelled  down  first,  or  that  has  tlio 
least  number  standing  at  the  end  of  the  lesson,  loses  tiie  battle. 

Malf-wiiy  Line. — Another  method  is  to  have  the  pupils 
stand  consecutivel}'  in  a  single  line,  each  one  having  an  oppo- 
nent at  both  sides;  then  mark  a  half-wa}'  line,  assign  the 
words  from  head  to  foot,  allowing  them  to  trap;  and  the 
part}'  which  at,  the  end  of  the  exercise  has  the  largest  number 
above  the  half-way  line,  wins  the  victory. 

Keeping  Tallif. — Another  method  is  to   have  scorers  ap 
pointed  to  keep  a  record  of  the  words  missed  by  both  sides, 
as  in  a  base-ball  match,  the  contest  being  determined  b}'  the 
tally.     All  of  these  methods  i)ossess  advantages,  and  ma}'  be 
used  to  give  variety  and  interest  to  the  exercise. 

V.  Practical  Course  in  Orthography. 

Having  explained  the  two  methods  of  teaching  orthography 
somewhat  in  detail,  we  now  proceed  to  present  some  suggestions 
for  actual  instruction  in  orthography  in  our  schools.  This  course 
should  be  based  on  the  following  principles:  1.  Teach  first  by 
un-iting  ivords  rather  than  by  oral  spelling.  2.  Write  words,  at 
first,  in  sentences  rather  than  in  columns.  3.  Use  familiar  words 
of  which  pupils  know  the  meaning.  -4.  Impress  mental  pictures 
of  words  on  the  memory.  5.  Cultivate  the  habit  of  observing 
the  orthography  of  words.  6.  Call  attention  to  orthography  in 
all  the  branches  of  study. 

Written  Spelling. — Young  pupils  should  begin  orthography 
by  copying  words.     They  should  first  copy  the  sentences  as  found 


TEACHING    ORTHOGRAPHY.  163 

in  their  reading  books.  Their  attention  should  be  called  to  the 
capital  letters  and  punctuation  marks,  and  thej  will  learn  to 
punctuate  and  use  capitals  almost  unconsciously.  Words  may 
also  be  given  for  them  to  incorporate  into  sentences  of  their  own 
construction.  With  young  pupils  do  not  call  attention  to  mis- 
spelled words,  but  erase  them  and  write  the  words  correctly. 
Older  pupils  may  have  words  assigned  to  them  to  write  in  col- 
umns, as  explained  under  the  description  of  the  written  method 
of  teaching  orthogra|jhy. 

Oral  SptlUng. — A  little  oral  spelling  may  be  introduced 
somewhat  incidentally  during  the  first  two  or  three  years.  With 
older  pupils  oral  spelling  may  be  more  frequent.  In  spelling  or- 
ally, pupils  should  be  required  to  form  mental  pictures  of  words 
and  then  describe  them  by  naming  the  letters.  This  picturing 
of  words  in  the  mind  will  be  found  to  be  a  most  interesting  and 
valuable  exercise,  and  is  essential  to  good  spelling.  During  the 
second  or  third  year  phonetic  spelling  may  be  begun ;  and  as  the 
pupil  acquires  skill  in  phonic  analysis  he  should  be  taught  to  rep- 
resent the  sounds  of  the  letters  by  the  diacritical  marks. 

The  Spelliiif/  UooA-.— With  beginners  the  best  spelling  book 
is  the  school  reader.  With  more  advanced  pupils  the  use  of  a 
good  "spelling  book"  will  be  found  of  great  convenience.  Such 
a  book  contains  a  list  of  words  that  the  pupil  will  use  in  practical 
life,  many  of  which  may  not  be  found  in  his  reading  books.  It 
will  also  be  more  convenient  for  him  to  study  a  "spelling  lesson" 
from  the  speller  than  from  the  reader.  Care  should  be  taken  in 
using  the  spelling  book  that  the  pupil  understands  the  meaning 
of  the  words  he  spells.  This  can  be  secured  by  requiring  him  to 
define  them  or  use  them  in  sentences.  Advanced  pupils  should 
be  encouraged  to  study  the  dictionary  in  order  to  perfect  them- 
selves in  spelling. 

PiipiVs  Preparation.— ^^^  older  pupil  should  be  required 
to  make  careful  preparation  for  his  spelling  lesson.  In  studying 
it,  he  should  not  depend  upon  calling  the  names  of  the  letters 
and   thus   trying   to  fix   them   in   his  memory;  but  he  should 


164  METHODS    OF   TEACHING. 

notice  carefully  the  structure  of  the  words,  and  endeavor  to 
stamp  a  picture  of  each  word  on  his  memory.  He  should 
always  write  the  words  of  the  lesson,  even  in  preparing  for  an 
oral  exercise,  as  he  can  in  this  way  better  fix  them  in  the  mind. 

Raines  of  Common  Things. — The  teacher  will  find  it  an 
interesting  and  profitable  exercise  to  require  pupils  to  spell  the 
names  of  common  things.  At  the  close  of  a  lesson,  the  teacher 
may  say,  To-morrow  we  will  spell  the  names  of  aU  the  things 
found  in  the  parlor,  or  the  kitchen,  or  on  a  farm,  or  in  the 
barn,  or  in  a  carpenter's  shop,  or  a  blacksmith's  shop,  etc. 
The  names  of  flowers,  of  trees,  of  articles  of  dress,  of  persons, 
etc.,  make  an  interesting  and  valuable  exercise. 

Words  often  Misspelled. — The  teacher  should  select  words 
often  misspelled,  and  drill  the  pupils  upon  them.  With 
younger  pupils  these  are  the  little  words;  as,  there,  their, 
which,  ivhere,  until,  some,  many,  piece,  very,  any,  pity, 
forty,  right,  great,  every,  neither,  weather,  whether,  etc. 
These  are  the  words  which  they  use  in  composition,  in  writ- 
ing letters,  etc.;  and  the}^  should  be  among  the  very  first 
which  the  pupils  learn  to  spell.  It  is  a  mistake  to  have  pupils 
spelling  words  of  three  or  four  syllables  which  they  very  sel- 
dom use,  while  they  cannot  spell  the  little  words  of  every-day 
life.  Drill  them  also  in  words  of  like  pronunciation  and  unlike 
orthograph}^,  a  list  of  which  can  easily  be  found  or  made  by 
the  teacher. 

In  all  Branches. — Attention  should  be  given  to  spelling 
in  all  the  branches.  Frequently  require  pupils  to  spell  some 
technical  term  in  arithmetic  or  grammar,  a  name  in  geogra- 
phy or  history,  etc.  "We  should  make  orthography  specially 
prominent  in  the  reading-lesson.  This  will  beget  in  pupils  a 
habit  of  looking  at  the  structure  of  words,  which  will  be  of 
great  value  to  them,  for  it  is  in  this  way  that  literaiy  men 
and  women  become  skilled  in  orthography-. 

Association. — Words  whose  orthography  it  is  difficult  to 
remember   may   be   associated   with    other    words    similarly 


TEACHLXQ   ORTHOGRAPHY.  165 

spelled,  whose  orthograph}^  is  remembered.  Thus,  a  gentle- 
man who  had  a  difficult}'  with  piece,  remembered  whether  the 
i  or  e  came  first  bj'  associating  it  with  pie  in  the  expression, 
"  a  piece  of  pie."  A  lad}-  who  could  not  remember  whether 
there  were  one  or  two  e'*;  before  the  a  in  agreeable,  was  told 
to  associate  it  with  the  fact  that  there  were  two  agreeable  gen- 
tlemen present  when  she  asked  the  question  ;  and  she  after- 
ward had  no  difficulty  with  the  word.  A  student  remembered 
that  there  was  no  e  before  the  m  in  Judgment  by  the  picture  of 
the  word  on  the  blackboard  with  a  line  drawn  by  the  teacher 
through  the  e  (J udgement)  vf^hich  the  pupil  had  incorrectly  put 
in  it.  A  little  mortification  with  the  misspelling  of  a  word, 
as  many  persons  have  ex^jerienced  with  the  word  separate, 
will  serve  to  impress  the  correct  spelling.  Some  artifices 
like  these  are  of  value  in  those  idiosyncrasies  by  which  we 
are  doubtful  of  special  words. 

IFords  to  Compose  Words. — An  interesting  exercise  in 
orthography  is  presented  by  giving  words  for  the  pupils  to 
compose  other  words  out  of  their  letters,  using  the  letters  no 
ofteuer  than  they  occur  in  the  given  word.  Thus,  the  word 
treason,  in  this  way,  will  give  over  100  words  ;  Baltimore, 
over  200  ;  comfortable,  over  300  ;  manufactory,  over  500.  A 
prize  was  offered  by  the  Christian  Union  for  the  largest  num- 
ber of  words  formed  from  subscription ;  the  successful  com- 
petitor made  1049  words.  The  pupils  may  also  be  allowed  to 
use  the  letters  of  the  word  as  often  as  they  wish  in  forming 
new  words.  In  this  way  a  pupil  of  our  Model  School  made 
out  of  the  word  Baltimore  2184  words. 

Rules  for  Spellinff. — English  Orthography  is  so  irregular 
that  it  acknowledges  verv  little  allegiance  to  rule.  Most 
rules  that  can  be  given  are  subject  to  so  many  exceptions  that 
it  is  usually  easier  to  learn  to  spell  words  directly  than  to 
remember  the  rules  and  their  exceptions.  No  one,  therefore, 
can  expect  to  learn  to  spell  by  rule.  There  are,  however,  a  few 
rules  that  admit  of  very  wide  application,  and  are  subject  to 


166  METHODS   OF   TEACHING. 

80  few  exceptions  that  they  may  be  used  with  advantage.  The 
most  important  of  these  rules  relate  to  the  omission  or  retention 
of  the  final  letter  of  a  word  on  receiving  a  suffix.  They  may  be 
stated  as  follows : 

1.  Final  e  is  omitted  in  adding  a  suflBx  beginning  with  a  vowel,  and  is 
retained  in  adding  a  suffix  beginning  witli  a  consonant. 

2.  Final  y  when  preceded  by  a  consonant,  is  changed  to  i  in  adding  a  suffix ; 
but  when  preceded  by  a  vowel,  it  is  not  changed  in  adding  a  suffix. 

3.  A  single  final  consonant  is  doubled  on  adding  a  suffix, — when  the  con- 
sonant is  preceded  by  a  single  vowel,  and  the  suffix  begins  with  a  vowel, 
and  the  final  syllable  is  accented. 

4.  The  final  consonant  is  not  doubled, — if  it  is  not  preceded  by  a  single 
Towel,  or  if  the  suffix  does  not  begin  with  a  vowel,  or  if  the  word  is  not 
accented  on  the  last  syllable. 

5.  Of  words  ending  in  ceous  or  cious, — those  which  relate  to  matter  end  in 
eeous,  and  all  others  in  cious.  Silicious,  sometimes  written  siliceous,  is  an 
apparent  exception. 

False  Orthography. — The  use  of  false  orthography  has 
been  recommended  by  some  authors  to  aid  the  pupil  in  learn- 
ing to  spell.  Such  exercises  are  supposed  to  bear  the  same 
relation  to  learning  orthography  as  false  syntax  in  grammar 
does  to  learning  to  speak  and  write  correctly.  The  principle  is 
that  we  learn  the  right  by  seeing  the  wrong  ;  the  correct  usage 
by  seeing  the  incorrect  usage.  It  is,  however,  a  question 
whether  such  exercises  are  not  a  disadvantage.  Teachers  who 
have  used  them  say  that  pupils  are  liable  to  confound  the  cor- 
rect and  incorrect  forms,  that  the  picture  of  the  mis-spelled 
word  sometimes  clings  to  the  memory  and  becomes  a  model  to 
mislead  the  pupil. 

Finally,  cultivate  an  interest  among  your  pupils  in  spelling, 
and  manifest  an  interest  in  it  yourself  Make  them  feel  that 
poor  spelling  is  a  disgrace  ;  and  lead  them  to  see  that  correct 
spelling  is  a  characteristic  of  a  cultivated  lady  and  gentleman 
Train  them  to  the  habit  of  noticing  the  orthography  of  word? 
in  their  reading,  for  it  is  in  this  way  that  men  and  women  reallj 
learn  to  spell. 


CHAPTER   VI. 

TEACHING  READING  OR  ELOCUTION. 

READING,  or  Elocution,  is  the  art  of  giving  proper  oral 
expression  to  thought  and  sentiment.  It  is  the  art  of 
correct  vocal  delivery  with  the  speaking  tones  of  the  voice  in 
distinction  from  the  singing  tones.  Reading  and  Elocution 
are  very  nearl}^  synonymous,  though  the  latter  term  is  gener- 
ally applied  to  the  higher  departments  of  Reading.  Silent 
Reading,  or  reading  to  one's  self,  is  not  included  in  the  defi- 
nition, as  this  is  merely  seeing  the  thought  through  the  words, 
and  not  oral  delivery. 

Importance Reading    is   one   of    the    most    important 

branches  in  our  schools.  This  importance  ma}'  be  somewhat 
appreciated  by  comparing  it  with  other  branches,  as  arithmetic, 
grammar,  music,  etc.  Many  persons  would  rather  be  a  great 
elocutionist  than  a  great  mathematician,  grammarian,  or  mu- 
sician. The  great  actors  have  been  as  highly  honored  as  the 
great  musicians;  Charlotte  Cushman  has  perhaps  as  enduring 
a  fame  as  Jenny  Lind.  The  eminent  orators  stand  as  high  in 
public  appreciation  as  the  eminent  mathematicians ;  though 
part  of  this  eminence  is  due  to  the  thought  and  sentiment  ex- 
pressed, rather  than  to  the  delivery.  Reading  is  a  fine  art. 
and  should  be  regarded  as  a  valuable  accomplishment ;  with 
proper  attention  to  it,  we  could  make  reading  and  reciting  as 
popular  in  society  as  plajnng  the  piano  or  singing. 

Reading  has  been  very  poorly  taught  in  most  of  our 
schools.  In  the  colleges,  until  quite  recently,  no  instruction 
whatever  was  given  in  delivery.  In  our  seminaries  and  acad- 
emies, though  there  were  special  teachers  of  mathematics, 
natural   sciences,  languages,   etc.,  any  one  was   regarded   as 

(167) 


168  METHODS   OF   TEACHING. 

c<)mpetent  to  heai-  the  reading  classes.  The  pupils  in  our 
public  schools  were  ''taught  to  read,"  but  it  was  really  a 
"calling  of  words"  and  not  reading  in  its  true  sense.  The 
best  work  in  this  branch  has  been  done  in  our  Normal 
Schools,  and  their  influence  in  improving  the  methods  of 
teaching  reading  has  been  wide-spread  and  beneficial. 

We  should  make  a  special  study  of  reading,  and  endeavor 
to  excel  as  teachers  of  it.  Even  for  the  teacher's  own  culture 
and  success,  it  will  be  found  of  great  advantage.  Our  influ- 
ence will  depend  almost  as  much  upon  the  manner  of  our 
sa^'ing  things,  as  on  what  we  say.  In  social  life,  we  render 
ourselves  agreeable  and  iuci-ease  our  influence  by  an  attractive 
and  pleasing  manner  of  expression.  Business  success  depends 
largely  on  a  person's  address ;  and  influence  in  public  life  is 
to  a  large  extent  the  result  of  a  clear  and  forcible  expression 
of  thought.  A  public  speaker  should  be  a  good  elocutionist. 
The  great  orators  were  skilled  in  their  delivery,  as  well  as 
clear  and  forcible  in  their  style  of  composition.  It  is  reported 
of  Whitefield  that  he  could  move  an  audience  to  laughter  or 
tears  by  the  utterance  of  the  word  Mesopotamia.  Demos- 
thenes and  Cicero  cultivated  the  art  of  delivery  with  the  most 
assiduous  care,  and  were  masters  of  expression  as  well  as  of 
composition. 

Methods  of  Teaching — Methods  of  teaching  reading  may 
be  discussed  under  three  heads ;  the  Mental  Element,  the 
Vocal  Element,  and  the  Physical  Element. 

The  Mental  Element  is  that  by  which  we  understand  and 
feel  what  we  read.  It  includes  the  Intellectual  and  the  Emo 
tional  elements.  The  Intellectual  Element  is  that  by  which 
■ive  understand  what  we  read.  The  Emotional  Element  is  that 
by  which  we  feel  and  api>reciate  what  we  read.  Both  of  these 
are  necessary  conditions  for  correct  and  effective  reading. 

The  Vocal  Element  is  that  which  pertains  to  the  voice.  It 
embraces  Pronunciation  and  Modulation.  Pronunciation  is 
the  art  of  giving  correct  utterance  to  individual  words.     It 


TEACHING  READING  OR  ELOCUTION.       169 

embraces  Articulation  and  Accent,  both  of  which  have  been 
discussed.  Modulation  has  reference  to  the  variations  of  the 
voice  in  reading  and  speaking.  It  embraces  Quantity,  Com- 
pass, Quality,  and  Time,  each  of  which  has  its  appropriate 
subdivisions. 

The  Physical  Element  is  that  which  pertains  to  the  body  and 
its  members.  It  includes  Breathing,  Posture,  Gesture,  and 
Facial  Expression. 

Frinciples  of  Teaching — There  are  several  fundamental 
principles  that  will  be  of  advantage  to  teachers  of  reading. 
The  most  important  of  these  are  Natural  Expression,  Imitation, 
Principles,  and  Correcting  Errors. 

1.  Natural  Expression. — The  fundamental  principle  in  teach- 
ing reading  is  that  of  natural  expression.  The  constant  effort  of 
the  teacher  should  be  to  have  the  pupils  read  naturally,  or  to  read 
as  they  talk.  The  following  ideas  should  be  kept  constantly  before 
the  pupils'  minds. 

Talking  is  the  natural  expression  of  one^s  own  thoughts ;  read- 
ing is  the  natural  expression  of  written  or  printed  thought. 
Written  or  printed  thought  should  be  expressed  in  the  same  way 
as  one  would  express  it  if  it  were  his  own  thought. 

Good  conversation  is  thus  the  basis  of  good  reading.  Good 
reading  is  reading  as  one  talks.  To  read  well  a  person  should 
express  himself  just  as  he  does  in  natural  conversation.  If  his 
conversational  style  is  faulty,  the  first  step  is  to  correct  and  im- 
prove it. 

To  read  naturally,  the  pupil  must  make  the  thought  of  the 
author  his  own  thought,  and  then  express  it  just  as  he  would  if  he 
had  originated  it.  The  reader  must  re-create  the  ideas  of  the 
author  and  stamp  them  with  his  own  personality,  and  then  ex- 
press them  as  if  they  were  his  ovm  and  not  another's. 

2.  Imitation. — Reading  is  an  art,  and  like  other  arts  must  be 
taught  partly  by  imitation.  We  learn  to  talk  by  imitating  our 
parents  and   other  members  of  the  household ;  and  we  learn  to 

write  by  imitating  written  or  printed  forms.      So  in  order  to 

8 


170  METHODS  OF  TEACHING. 

learn  to  read  well,  we  must  hear  good  reading.  The  teacher, 
therefore,  should  read  for  his  pupils  and  have  them  imitate  his 
reading,  being  careful  to  avoid  all  mannerisms  that  may  vitiate 
their  style  or  interfere  with  natural  expression. 

The  teacher  should  be  a  good  reader,  that  he  may  present  a 
correct  model  for  his  pupils.  He  must  often  lead  them  to  cor- 
rect expression  by  having  them  imitate  his  own  reading  of  a 
sentence  or  selection.  This  is  the  more  necessary  from  the  fact 
that  there  are  many  things  in  the  reading  book  so  different  from 
the  ordinarv  topics  of  conversation  that  pupils  need  the  model 
of  the  teacher's  voice  and  manner  to  guide  them. 

3.  Principles. — There  should  also  be  some  general  principles  to 
guide  a  pupil  in  reading.  By  a  principle  of  reading  is  meant 
some  general  law  which  can  be  readily  applied  to  the  particular 
forms  of  discourse  we  meet  with  in  literature.  Rules  of  reading 
have  been  criticised,  and  properly  so,  fur  no  one  can  learn  to 
read  correctly  by  rule.  A  principle,  however,  is  more  flexible 
than  a  rule,  and  will  be  fi)und  of  very  great  value,  with  the 
more  advanced  pupils,  in  learning  to  read. 

4.  Correcting  Errors. — The  teacher  must  also  rely  on  the  cor- 
rection of  errors  for  instruction  in  the  art  of  reading.  He  must 
notice  carefully  the  errors  of  pupils,  and  correct  them.  He 
should  not  merely  call  attention  to  these  mistakes,  but  should 
train  the  pupils  in  correcting:  them  until  they  have  overcome  the 
old  habit  and  acquired  the  new  one.  It  is  sometimes  well  to 
imitate  the  mistake  of  the  pupil ;  his  attention  being  thus  called 
to  it,  he  will  usually  correct  it  himself. 

Teaching  Primary  Reading. 

The  course  in  Primary  Reading  includes  such  instruction  in 
the  art  of  reading  as  is  required  by  the  majority  of  the  children 
in  our  public  schools.  Suggestions  for  this  course  will  be  pre- 
sented under  the  three  general  divisions  named. 

1.  The  Mental  ElExMENT. — The  Mental  Element  lies  at  the 
basis  of  good  reading.     The   mind   thinks   the   thought,  and  in 


TEACHING   KEADINQ   OR   ELOCUTION".  171 

correct  reading  the  voice  should  express  just  what  is  in  the  mind. 
The  pupil  should,  therefore,  understand  that  good  reading  is 
merely  having  something  in  his  mind  and  telling  it. 

All  the  principles  of  reading  have  their  origin  in  the  mind, 
and  are  applied  by  it.  The  most  important  of  these  principles, 
which  may  be  regarded  as  the  conditions  of  good  reading,  are 
those  of  Comprehension,  Appreciation,  and  Conception. 

1.  Comprehension. — The  first  law  of  good  reading  is  that  of 
comprehension.  The  pupil  must  be  led  to  see  that  reading  is  not 
calling  words  in  the  hook,  but  merely  telling  what  he  thinks  and 
Jeels.  He  must  be  taught  to  read  from  his  thought  and  not  from 
his  book.  In  order  to  do  this  he  must  be  trained  to  the  habit  of 
getting  the  thought  of  the  selection  he  is  reading. 

1.  See  that  the  pupil  understands  the  meaning  of  the  words. 
Go  over  the  sentences  and  paragraphs  and  call  attention  to  such 
words  as  the  pupil  may  not  understand.  Have  the  pupil  use  the 
words  in  sentences,  to  see  that  they  are  understood. 

2.  See  also  that  the  pupils  understand  the  thought  expressed 
in  the  sentences.  Have  them  state  the  thought  in  their  own  words. 
Require  them  to  look  at  a  sentence  and  grasp  it  as  a  whole  before 
attempting  to  give  it  expression. 

3.  Require  pupils  to  analyze  each  sentence  and  paragraph,  and 
point  out  the  prominent  ideas,  so  that  they  may  know  where  to 
place  the  emphasis.  When  they  do  not  see  the  prominent  ideas 
call  attention  to  these  ideas  by  appropriate  questions. 

4.  Require  pupils  to  study  their  reading  lessons.  Examine 
them  on  the  lesson  to  see  that  they  understand  it  before  permit- 
ting them  to  read.  Explain  such  things  as  are  not  understood, 
especially  figures  of  Rhetoric,  such  as  similes,  metaphors,  person- 
ifications, historical  and  classical  allusions,  etc. 

5.  Do  not  go  through  the  book  too  rapidly.  In  teaching  read- 
ing it  is  a  good  maxim  to  "make  haste  slowly."  Keep  pupils  at 
a  selection  until  they  are  quite  familiar  with  it.  The  better  they 
know  it  the  better  they  can  read  it.  Let  the  first  aim  be  to 
make  the  pupils  thoroughly  comjjrehetid  what  they  are  reading. 


172  METHODS   OF   TEACHING. 

2.  Appreciation. — The  second  law  of  good  reading  is  that  of 
appreciation.  Pupils  should  be  led  to  appreciate  the  sentiment 
of  what  they  read.  The  voice  should  manifest  the  feeling  as  well 
as  the  thought;  the  heart  should  speak  in  the  voice  as  well  as  the 
head.  Reading  without  feeling  in  it  is  a  cold  mechanical  thing 
without  beauty  or  power. 

1.  To  awaken  an  appreciation,  see  that  there  is  a  full  and 
complete  comprehension  of  the  subject  read.  What  is  not  un- 
derstood cannot  be  very  well  appreciated  ;  a  clear  idea  in  the 
mind  naturally  awakens  some  corresponding  feeling  in  the  heart. 

2.  Try  to  make  the  appreciation  so  full  as  to  result  in  a  com- 
plete assimilation  of  the  thought  or  sentiment.  Lead  the  pupil 
to  make  the  thought  or  sentiment  /m  own,  as  if  it  were  the  pro- 
duct of  his  own  mind  and  heart ;  and  he  will  then  read  it  as  if 
he  were  telling  something  he  had  thought  or  felt. 

3.  To  secure  this  condition  of  appreciation  and  assimilation 
usually  requires  careful  culture.  It  is  a  matter  of  taste,  and 
the  culture  of  taste  is  often  a  slow  process.  Try  to  lead  the 
pupil  to  see  what  is  beautiful  and  admirable  in  thought  and  sen- 
timent ;  to  have  his  heart  throb  responsive  to  the  beautiful  image 
or  touch  of  pathos  expressed  in  the  author's  lines. 

4.  Do  not  allow  pupils  to  read  subjects  that  are  not  suited  to 
their  appreciation.  Such  sentiments  as  "  Contentment,"  "  Patri- 
otism," "Melancholy,"  "Aristocracy,"  etc.,  are  foreign  to  the 
heart  of  a  child,  and  such  subjects  should  not  be  given  him  to 
read.  He  can  appreciate  "  the  pleasures  of  coasting,"  "  sorrow  at 
the  loss  of  a  pet  bird,"  etc.,  and  his  voice  will  throb  in  unison 
with  his  beating  heart  as  he  reads  of  these  things. 

3.  Conception. — Pupils  when  reading  should  form  a  clear  and 
vivid  conception  of  the  subject.  Young  children  describe  what 
they  have  seen  with  graphic  effect,  because  the  picture  of  what 
they  are  describing  stands  before  their  mind  as  they  are  talking. 
Lead  them  to  picture,  in  the  same  way,  what  they  read,  and  they 
will  also  express  it  vividly  and  naturally. 

1.  Require  pupils  to  form  mental  pictures  of  such  things  as  can 


TEACHING   READING   OR   ELOCUTION.  173 

be  represented  by  the  Imagination.  If  they  read,  "  I  see  a  bird 
in  a  tree,"  they  should  form  in  the  mind  a  picture  of  the  tree 
and  the  bird  in  it.  If  they  read  of  "a  boy  fishing,"  they  should 
see  the  water,  and  the  boy  in  the  act  of  catching  fish.  If  the 
lesson  is  about  "a  horse  running  away,"  require  them  to  picture 
the  horse  running  just  as  they  would  if  they  had  seen  it  and 
were  describing  an  actual  run-a-way. 

2.  With  the  more  advanced  pupils,  take  such  selections  as  "A 
Leap  for  Life,"  by  Colton,  or  "  The  Day  is  Done,"  by  Long- 
fellow,  or  "  Abou  Ben  Adhem,"  by  Leigh  Hunt;  and  require  the 
pupils  to  form  pictures  in  the  mind  as  they  read  or  recite  these 
selections.  Test  the  power  to  picture  by  asking  them  to  describe 
what  is  in  the  mind  when  they  read. 

3.  Where  a  mental  picture  of  the  subject  can  not  be  formed, 
try  to  make  the  abstract  conception  as  clear  and  real  as  possible. 
See  that  the  thought  or  sentiment  is  distinctly  conceived.  When 
the  conception  is  distinct  and  real,  the  heart  will  respond  to  the 
thought,  and  the  voice  will  instinctively  and  truthfully  portray 
the  sentiment. 

4.  This  exercise  of  vivid  conception  will  be  found  of  great 
value  in  teaching  reading.  It  gives  a  reality  to  the  subject  in 
the  pupils'  minds  which  makes  their  reading  not  a  mere  calling 
of  words,  but  a  real  relation  of  the  thought  or  incident  expressed 
by  the  author.  It  may  be  stated  as  a  maxim  that  vividness  of 
conception  is  a  golden  key  to  truthful  and  effective  expression. 

II.  The  Vocal  Element.— The  next  step  is  to  attain  a 
proper  use  of  the  voice  in  delivery.  First,  there  should  be  exer- 
cises to  train  the  voice  in  the  correct  utterance  of  sounds.  Second, 
care  should  be  taken  that  all  the  words  be  correctly  pronounced. 
Third,  the  form  of  expression  of  words  in  sentences  should  be 
correct  and  pleasing.  These  three  points  will  be  considered 
under  the  heads  of  Exercises,  Pronunciation,  and  Expression. 

1.  Exercises. — Pupils  require  some  exercises  to  give  flexibility 
and  precision  to  the  voice.  These  exercises  train  the  ear  to  a 
delicacy  of  perception  that  will  enable  the  pupil  to  correct  his 


174  METHODS   OF   TEACHING. 

errors  and  improve  his  utterance.  They  will  also  give  such  a 
control  over  the  voice  that  it  can  be  readily  adapted  to  the  differ- 
ent selections  read.     The  fullowino:  exercises  are  sussrested. 

1.  Train  the  voice  in  respect  to  force,  pitch,  and  rate.  Use  the 
vowel  sounds  (vocals)  a,  a,  a,  a,  e,  c,  etc.,  for  this  purpose.  Unite 
these  vocals  with  the  consonant  sounds  (sub-vocals),  as  ha,  hd,  ha, 
etc.     Drill  also  on  special  words ;  as  arm,  gold,  etc. 

2.  For  exercises  in  Force,  require  the  pupils  to  repeat  the 
sounds  with  varying  force,  from  soft  to  loud.  Have  similar  exei- 
cises  on  words  and  on  sentences  appropriately  selected. 

3.  For  exercises  in  Pitch,  have  the  pupils  repeat  the  vocals 
on  different  degrees  of  the  musical  scale  from  low  to  high.  Have 
them  sing  the  musical  scale,  and  use  it  in  exercises  on  pitch. 
Drill  on  slides  or  inflections,  both  rising  and  falling. 

4.  For  a  drill  in  Time,  use  the  vocals  and  words,  repeating  them 
with  shorter  and  longer  time.  Have  them  also  read  sentences 
with  different  degrees  of  time.     Djill  also  on  pauses. 

5.  For  a  drill  in  Emphasis,  use  properly  selected  sentences 
containing  emphatic  words.  Sentences  containing  contrasted 
emphasis  will  be  of  special  use  in  this  exercise.  Lead  them  to  see 
that  the  prominence  of  the  idea  determines  the  emphasis. 

2.  Pronunciation. — The  pupil  should  be  able  to  pronounce 
readily  and  correctly  all  the  words  in  the  reading  lesson  before 
he  begins  to  read.  Bad  reading  and  bad  habits  in  reading  often 
result  from  the  pupils  stumbling  over  unfamiliar  words. 

1.  See  that  pupils  are  able  to  pronounce  words  at  sight.  Re- 
quire them  to  know  the  words  at  a  glance,  so  that  they  can  speak 
them  in  reading  without  hesitation  or  stammering. 

2.  It  is  often  well  to  go  over  the  sentence  or  paragraph  and 
have  the  pupils  pronounce  the  words  before  they  attempt  to  read 
it.  They  may  sometimes  begin  at  the  latter  part  of  the  para- 
graph and  "  pronounce  the  words  backward." 

3.  With  the  more  advanced  classes,  before  reading  anew  les- 
son, go  over  it  and  have  the  pupils  pronounce  the  unfamiliar  or 
difficult  words.  Some  of  these  may  be  written  on  the  blackboard 
to  aid  the  pupil  in  remembering  them. 


TEACHING    READING   OR   ELOCUTION.  175 

4.  Careful  attention  should  be  given  to  articulation  and  accent 
Let  the  teacher  be  particular  to  secure  clear  and  distinct  enun- 
ciation. Do  not  permit  a  drawling  tone  in  the  utterance  of 
words,  nor  a  slovenly,  careless  or  unrefined  pronunciation, 

3.  Ex2)ression. — The  proper  use  of  the  voice  in  vocal  utterance 
is  the  final  step  in  reading.  Thi.s  is  a  high  accomplishment,  and 
demands  great  care  for  its  attainment.  AVhat  has  been  previ- 
ously explained  is  all  ])reparatory  to  this  final  object,  but  a  few 
special  suggestions  on  expression  will  be  of  value  to  the  teacher. 

1.  The  fundamental  principle  of  expression  is  that  the  v(nce 
exactly  express  the  thought  uhich  is  in  the  viind.  To  secure  this, 
see  that  there  is  comprehension,  appreciation  and  conception; 
and  then  that  the  force,  pitch  and  rate  are  such  as  the  sentiment 
requires. 

2.  See  that  the  piipils  read  naturally,  as  they  ivould  talk,  pro- 
vided they  talk  correctly.  Let  the  natural  expression  of  the  pupil 
be  the  basis  of  his  method  of  reading.  If  he  does  not  read  natur- 
ally, require  hira  to  look  off  his  book  and  tell  you  the  subject. 

3.  Be  careful  to  secure  a  proper  variety  in  the  tone  of  the  voice, 
as  in  good  natural  conversation.  Do  not  allow  children  to  use 
the  stilted  and  mechanical  tone  so  common  in  our  schools,  nor  the 
monotonous  sing-song  in  which  young  persons  often  read.  Dis- 
card by  all  means  the  well  known  "school-room  tone." 

4.  See  that  the  emphasis  is  properly  placed,  as  misplaced  em- 
phasis is  one  of  the  common  faults  of  reading.  Be  sure  that  the 
pijpil  fully  understands  the  subject  he  is  reading,  and  sees  which 
are  the  important  ideas.  Lead  the  pupil  to  see  what  ideas  are 
most  important,  and  he  will  give  correct  emphasis. 

5.  Notice  with  care  that  the  pauses  be  properly  placed,  and 
are  of  the  proper  length.  Lead  the  pupils  to  see  that  it  is  the 
thought,  and  not  the  marks  of  punctuation,  that  determines  the 
place  and  length  of  the  pauses.  Show  them  also  the  value  of  the 
pause  after  and  before  the  emphatic  word. 

6.  See  also  that  the  slides  or  inflections  are  properly  used. 
Lead  pupils  to  see  that  the  sense  will  determine  whether  the  slide 


176  METHODS    OF    TEACHING. 

is  downward  or  upward.  Call  attention,  when  they  are  in  doubt 
about  the  slide,  to  the  manner  in  which  thev  would  naturally 
express  themselves  if  they  were  telling  the  subject.  Do  not  allow 
the  use  of  the  circumflex  where  it  is  not  required  by  the  sense. 

7.  See  also  that  there  is  proper  natural  melody  in  the  use  of  the 
voice.  Be  careful  that  there  is  no  jerkiness  or  abruptness  in  the 
use  of  the  voice  ;  but  a  natural  melodious  flow  of  tone  that  gives 
a  sense  of  musical  beauty  to  their  expression. 

III.  The  Physical  Element. — The  Physical  Element  in 
reading  is  that  which  pertains  to  the  body.  It  is  of  special  value 
in  recitation  and  oratory,  but  needs  little  attenti(»n  in  ordinary 
reading.  Only  a  few  suggestions  will  therefore  be  presented 
under  this  head. 

1.  Have  pupils  stand  erect,  with  the  book  in  the  left  hand,  so 
that  the  right  hand  may  be  free  to  turn  the  leaf  when  needed. 
While  reading  the  right  hand  should  hang  at  the  side. 

2.  See  that  the  feet  are  in  a  natural,  easy  position,  and  that  the 
body  is  erect  with  the  shoulders  thrown  gently  back  to  give  free- 
dom to  the  organs  of  the  chest. 

3.  Permit  no  lounging  or  leaning  upon  the  desk  or  against  the 
wall,  or  standing  in  any  awkward  or  ungraceful  attitude. 

Finally,  teachers,  if  you  see  that  your  pupils  stand  in  a  proper 
attitude;  that  they  comprehend,  appreciate  and  conceive  what  they 
read  ;  that  they  read  naturally,  with  correctness  of  force,  rate,  pitch, 
emphasis,  slides,  pauses,  and  melody;  you  will  be  a  successful 
teacher  of  reading  in  our  public  schools. 

II.  Teaching  Advanced  Heading. 

The  course  in  Advanced  Reading  shows  the  principles  upon 
which  the  art  is  based,  and  aims  to  inculcate  the  practice  from 
the  theory.  It  embraces  a  brief  treatise  upon  Elocution,  and 
prepares  for  recitation  and  declamation  as  well  as  reading.  It  is 
presented  under  the  three  elements  already  named;  viz.: 

I.  The  Mental  Element.        II.  The  Vocal  Element. 
III.  The  Physical  Element. 


TEACHING    KEADIXG    OK    ELOCUTION.  177 


I.     The  Mental  Element  in  Reading. 

The  Mental  Element  in  reading  is  that  by  which  we  under- 
stand and  feel  what  we  read.  It  includes  the  Intellectual  and 
Emotional  elements.  The  Intellectual  Element  is  that  by 
which  we  understand  what  we  read;  the  Emotional  Element  is 
that  by  which  we  feel  what  we  read.  Both  of  these  will  be 
brietly  considered. 

The  Intellectual  Element — A  pnj)il  should  understand 
what  he  reads.  No  one  can  read  correctly  what  he  does  not 
fully  comprehend.  He  may  pronounce  the  words  correctly, 
but  unless  he  comprehends  the  thought  he  is  endeavoring  to 
present,  it  will  be  merely  "  calling  words,"  not  reading.  This 
condition  of  good  reading  is  frequently  neglected.  Pupils  are 
allowed  to  read  without  having  any  idea  of  the  meaning  of 
what  they  are  reading.  Pupils  sometimes  speak  pieces  with- 
out any  clear  conception  of  the  ideas  and  sentiments  ex- 
pressed. The  artificial  and  unnatural  st3de  in  Avhich  young 
persons  read  is  largel}^  due  to  the  neglect  of  this  principle. 
Most  ridiculous  mistakes  are  sometimes  made  b}'  pupils  in 
endeavoring  to  read  that  which  they  do  not  understand,  or 
which  they  misunderstand. 

Pupils  should  be  required  to  prepare  their  reading  lessons 
as  they  do  other  lessons.  Every  pupil  should  study  his  read- 
ing lesson.  He  should  see  that  he  knows  the  meaning  of  the 
words,  the  idea  intended  to  be  expressed  by  the  author,  the 
general  character  of  the  sentiment,  the  meaning  and  force  of 
the  prominent  allusions,  rhetorical  figures,  etc.  It  will  be 
well  to  go  over  the  lesson  and  mark  the  emphasis,  slides, 
varieties  of  voice,  etc.,  appropriate  to  the  different  parts  of 
the  piece  to  be  read.  If  a  portion  of  it  were  entirely  or 
partly  committed  to  memory,  it  could  be  read  much  more 
readily  and  correctly.  It  is  said  that  the  great  orators  studied 
their  addresses  so  carefully  that  they  knew  just  what  words 
they  were  to  emphasize,  where  to  make  a  gesture,  etc. 
8* 


178  METHODS    OF    TEACUING. 

Teachers  should  examine  their  pupils  to  see  that  they  under- 
stand the  reading-lesson.  They  should  ask  them  questions 
upon  the  meaning  of  words,  upon  the  thought  intended  to  be 
presented,  upon  the  figures  and  allusions  that  may  be  used, 
upon  the  historical  or  biographical  references,  upon  the  gen- 
eral sentiment  of  the  piece,  and  upon  the  style  or  character  of 
the  composition.  Teachers  who  have  not  been  accustomed  to 
such  an  examination  will  be  utterly  surprised  at  the  ignorance 
and  thoughtlessness  of  pupils  in  this  respect.  Some  very 
amusing  and  ridiculous  mistakes  could  be  given,  illustrating 
the  necessity  of  such  questions.  Pupils  may  often  be  required 
to  give  the  sense  of  a  passage  or  paragraph  in  their  own  lan- 
guage, to  see  if  they  understand  it.  Be  especiall}'  careful  in 
their  reading  of  poetry,  that  it  is  not  a  sing-song  of  words, 
without  any  true  conception  of  the  meaning. 

The  teacher  should  explain  what  the  pupil  does  not  under- 
stand. He  should  explain  the  meaning  of  words,  sentences, 
allusions,  figures  of  rhetoric,  etc.,  which  the  pupil  has  not 
understood.  When  the  pupil  meets  such  expressions  as  the 
"  Archimedean  lever,"  or  the  "  Palladium  of  our  liberties,"  as 
found  in  Washington's  address,  or  the  "Niobe  of  nations,"  as 
found  in  Childe  Harold.,  etc.,  the  teacher  should  explain  the 
historical  fact  or  mythological  stor}^  from  which  they  are 
derived,  and  show  the  force  and  beauty  of  the  figure.  So  in 
reading  poetr3'^ ;  when  he  comes  to  such  passages  as  "  The 
darkness  falls  from  the  wings  of  night,"  or  "  Ai^d  Wind,  that 
grand  old  harper,  smote  his  thunder  harp  of  pines,"  or"  The 
Morn  in  russet  mantle  clad,  walks  o'er  the  dew  of  yon  high 
eastern  hill,"  etc.,  let  the  teacher  call  the  attention  of  the 
pupil  to  the  beauty  of  the  image  and  make  his  imagination 
picture  it  before  the  mind  as  it  was  seen  by  the  poet  who 
wrote  it.  The  heart  of  the  learner  can  in  this  way  be  thrillerl 
with  the  emotion  of  beauty,  the  imagination  be  trained,  and 
the  literary  taste  be  cultivated 

The  reading  books  should  be  adapted  to  the  pupils.     Foi 


TEACHIXG    READING    OK    ELOCUTION.  li'J 

young  pupils,  we  need  simple  descriptions,  lively  narratives, 
and  interesting  conversations  or  dialogues ;  for  more  ad- 
vanced pupils,  essay's,  reflections,  discussions,  orations,  etc., 
are  approi)riate.  This  principle  is  freciueutly  disregarded. 
]\Liny  authors  have  completely'  failed  in  the  ada[)tation  of  the 
reading  matter  of  their  books  to  the  capacity  and  taste  of  the 
puj)!!.  Only  a  few  seem  to  have  accomplished  the  difficult 
task  of  entering  into  the  sphere  of  child-life,  and  adapting 
their  writings  to  children. 

Teachers  must  also  be  careful  to  grade  the  books  properly 
for  tile  pupils.  The  general  fault  is  that  the  books  are  too 
difficult  for  the  classes  using  them.  The  pupil  is  often  in  the 
Fourth  Reader  when  he  should  be  in  the  Second  or  Third 
Reader.  In  such  cases  the  pupil  should  be  put  in  a  lower 
book  if  possible.  If  this  cannot  be  done,  the  easier  pieces 
should  be  selected,  and  the  pupil  drilled  on  them  until  he  is 
familiar  with  all  their  difficulties.  The  more  familiar  a  pupil 
is  with  a  piece  the  better  he  can  read  it. 

The  reading  teacher  should  be  a  good  scholar.  In  no  class 
does  a  teacher  require  so  much  general  culture  as  in  reading. 
He  needs  a  knowledge  of  history,  mythology,  rhetoric,  etc., 
in  order  to  explain  the  references,  allusions,  rhetorical  con- 
structions, etc.,  in  the  lesson.  The  reading  class,  properly 
taught,  can  be  made  the  most  interesting  and  profitable  class 
in  the  school.  More  can  be  done  for  literary  culture  here  than 
in  any  other  study.  Indeed,  many  a  person  has  received  his 
first  impulse  to  literary  culture  in  the  reading  class  as  taught 
by  some  earnest  and  enthusiastic  lover  of  literature. 

The  Emotional  Element. — A  pupil  should  not  only  un- 
derstand what  he  reads,  but  he  should  also  feel  and  appre- 
ciate it.  Literature  appeals  to  the  heart  as  well  as  to  the 
head.  The  reader  should  be  susceptible  to  all  the  various 
phases  of  sentiment,  and  feel  them  when  he  is  reading  so  that 
he  may  make  others  feel  them.  If  the  subject  is  pathetic,  his 
ueart  should  be  touched  with  pity;  if  it  is  humorous,  he  should 


180  METHODS    OF    TEACHING. 

appreciate  the  humor;  if  it  is  grand  and  sublime,  be  bbould 
feel  the  emotion  of  grandeur  stirring  in  his  soul.  This  point 
is  of  great  importance  in  all  the  higher  departments  of  read- 
ins,  and  demands  the  teacher's  attention. 

Pupils  do  not  usuall}'  feel  or  appreciate  what  they  read. 
They  will  read  one  st3'le  of  composition  in  just  about  the  same 
tone  and  pitch  as  another,  so  that  if  you  judged  the  composi- 
tion by  the  manner  of  reading,  you  could  not  tell  whether 
the}'  were  reading  a  funeral  sermon  of  Bossuet,  or  a  humorous 
description  bj'  Mark  Twain.  There  is  no  response  to  the 
touch  of  pathos  or  beaui 7,  no  heart-throb  to  the  poet's  line, 
or  the  orator's  sentiment ;  indeed  there  is  often  no  more  feel- 
ing than  if  a  talking  machine  were  repeating  the  words  of  the 
reading-book. 

The  teacher  should  call  the  attention  of  the  pupils  to  the 
sentiment,  and  endeavor  to  awaken  an  appreciation  of  it.  By 
appropriate  questions  and  explanations,  he  should  endeavor 
to  open  the  eyes  of  the  pupil  that  he  may  see,  and  unseal  his 
heart  that  he  may  feel,  those  touches  of  beauty  and  humor 
and  pathos  which  throb  in  the  poet's  line,  or  live  in  tiie 
orator's  phrase.  He  should  give  illustrations  of  the  different 
kinds  of  sentiments,  and  show  how  the  voice  and  mannei 
should  be  adapted  to  express  them.  In  a  word,  be  should 
train  his  pupils  so  that  they  may  feel  what  they  read,  as  well 
as  understand  it. 

Reading  books  should  be  adapted  in  sentiment  to  the  age 
of  the  pupils.  The  grander  sentiments  of  sublimity,  patri- 
otism, etc.,  are  not  suitable  to  children.  They  cannot  be 
expected  to  be  much  moved  by  a  description  of  the  "  Sublimity 
of  the  Starry  Universe,"  or  the  "Enjoyments  of  Content- 
ment," or  the  "  Remorse  for  Neglected  Opportunities."  The 
pathetic  and  many  forms  of  the  humorous,  however,  will  be 
readily  appreciated.  The  narration  of  interesting  events,  of 
dangers  in  field  or  forest,  of  hairbreadth  escapes,  of  the  rob- 
bing of  a  bird's  nest,  of  sorrow  at  the  loss  of  a  mother  or 


TEACHING    KKAlUNG    OK    ELOCUTION.  181 

sister,  etc.,  will  awaken  their  little  hearts  to  intense  feeling. 
The  compilers  of  text-books  on  reading  should  bear  this  in 
mind,  and  govern  themselves  in  their  work  accordingly. 

The  teacher  should  not  only  be  a  good  literary  sciiolar,  but 
he  should  also  possess  a  cultivated  taste.  Refinement  of 
mind,  a  heart  to  feel  and  appreciate  the  beautiful  and  good, 
will  enable  a  teacher  of  reading  to  touch  the  hearts  of  his 
pupils  and  cultivate  in  them  a  refinement  of  taste  which  will 
improve  both  their  character  and  their  reading.  The  teacher 
of  reading  should  therefore  take  special  pains,  by  the  study 
of  the  fine  arts  and  the  cultivation  of  that  which  is  beautiful 
and  noble  in  human  character,  to  acquire  such  refinement  of 
taste  and  feeling  as  shall  fit  him  for  the  highest  attainments 
in  his  hisrh  art. 


O' 


IT.    The  Vocal  Element  in  Eeading. 

The  Vocal  Element  in  reading  is  that  which  pertains  to  the 
voice.  It  is  the  fundamental  element  of  the  art  of  readinir. 
The  Mental  Element  is  merely  a  condition  for  good  reading, 
and  the  Physical  Element  an  accompaniment  of  it ;  but  the 
Vocal  Element  is  that  which  is  immediately  concerned  in 
reading.     It  is  the  basis  upon  which  the  art  is  established. 

The  importance  of  vocal  culture  in  reading  cannot  be  over- 
valued. The  excellence  of  reading  depends  mainly  upon  the 
character  of  the  voice.  When  the  voice  is  harsh  or  hard  and 
inflexible,  it  is  impossible  to  read  with  artistic  eflfect.  A  full, 
rich,  musical  voice  will  chain  the  attention  of  an  audience, 
independently  of  the  sentiment  expressed;  and  when  em- 
ployed in  the  expression  of  noble  and  soul-stirring  sentiments, 
its  influence  is  irresistible. 

Much  of  this  excellence  can  be  acquired  by  judicious  cul- 
ture. Though  some  voices  are  by  nature  richer  and  more 
musical  than  others,  yet  careful  training  will  remove  many 
defects  and  impart  flexibility  and  sweetness  in  a  remarkable 
degree.     Nearly  every  one  is  familiar  with  what  culture  and 


182  METHODS    OF    TEACHING. 

training  will  do  for  a  singer;  and  vocal  culture  is  as  necessarj' 
and  useful  to  the  reader  as  to  the  singer.  The  human  voice, 
in  the  hands  of  a  master,  will  attain  to  a  wondrous  strength 
and  richness  of  tone.  Practice  also  will  give  a  person  such  a 
command  over  his  voice  and  enable  him  to  use  it  with  such 
skill,  that  he  can  hold  the  attention  of  an  audience  by  the 
music  of  his  utterance,  and  thus  deepen  tlie  impression  of  the 
sentiments  he  may  express. 

The  Vocal  Element  embraces  four  things  ;  Quantidj,  Com- 
pass, Quality,  and  Time.  These  elements  are  usually  included 
under  the  head  of  Modulation.  Each  of  them  will  be  consid- 
ered somewhat  in  detail. 

I.  Quantity. — Quantity,  as  employed  in  reading,  has  refer- 
ence to  the  amount  or  volume  of  the  voice.  It  is  used  by 
some  elocutionists  to  mean  the  time  occupied  in  pronouncing 
a  word  or  syllable;  but  this  is  not  the  best  or  most  accept- 
able use  of  the  term.  Quantity  in  reading  is  a  general  term 
including  Force,  Emphasis,  Stress,  and  Slur. 

Quantity  of  voice  is  an  important  element  of  expression. 
Each  sentiment  has  its  appropriate  quantity,  and  the  quantity, 
if  properly  used,  will  indicate  the  sentiment.  Thus,  joy  is 
expressed  in  a  full  tone,  sorrow  in  a  subdued  tone  ;  modesty, 
humility,  shame,  doubt,  mystery,  etc.,  require  soft  and  sub- 
dued tones.  Anger  declares  itself  in  loud  tones,  confidence 
asserts  itself  with  a  full  voice,  secrecy  softens  the  tone  and 
speaks  with  muffled  voice  or  whisi)ered  accents. 

Force. Force  is  the  quantity  of  voice  used   in  reading  or 

speaking.  It  is  quantity  as  applied  to  vocal  delivery.  As 
used  here  it  has  reference  to  the  standard  force  of  the  voice 
in  reading  or  speaking. 

There  are  three  degrees  of  Force;  Soft,  Moderate,  and 
Loud.  .  Moderate  Force  is  the  ordinary  force  of  the  voice  in 
reading  and  speaking.  Soft  Force  is  less  force  than  the  ordi- 
nary quantity ;  and  Loud  Force  is  more  force  than  the  ordi- 
nary quantity.     These   are  not    fixed   degrees  of  force,  but 


TEACIIIXG    READING    UK    ELOCUTION.  183 

merely'  relative  distinctions.  Let  the  pupil  l)e  careful  not  to 
confound  loud  and  soft  with  high  and  luw,  which  are  degrees 
of  i)itch.  A  mistake  of  this  kind  often  leads  the  reader,  when 
he  designs  to  increase  his  force,  to  raise  his  voice  to  a  higher 
pitch,  thus  giving  a  higher  instead  of  a  louder  sound. 

Hoio  Tedch. — We  should  teach  reading  with  respect  to 
force  In-  Exercises,  Imitation,  and  Correcting  Errors. 

Exercises. — The  Exercises  recommended  to  cultivate  force 
are  as  follows  :  1.  A  frequent  drill  on  the  elementary  sounds; 
2.  A  drill  on  sentences  selected  for  the  purpose;  3.  Physical 
exercises  to  develop  the  general  health  and  strength. 

In  the  drill  on  the  elementary'  sounds,  we  should  begin  M'ith 
a  moderate  degree  of  force,  and  then  increase  the  force  gradu- 
ally to  the  limit  of  loudness,  being  careful  not  to  strain  or 
overtax  the  voice.  Having  reached  the  louder  tones,  pass 
gradually  from  these  to  the  softer  tones.  After  some  prac- 
tice in  this  wa}',  the  pupil  ma}'  begin  at  the  loud  tones  and 
pass  to  the  softer  ones  ;  or  he  may  practice  striking  at  once 
different  degrees  of  force  until  he  can  give  with  ease  and  pre- 
cision any  degree  of  force,  from  whispering  to  shouting. 

Similar  practice  with  well-selected  sentences  is  also  valuable. 
Let  the  same  sentence  be  given  with  varied  degrees  of  power; 
and  let  sentences  be  selected  requiring  variety  of  force  for 
their  natural  expression.  Such  exercises,  continued  for  a  few- 
months,  will  greatl}'-  enlarge  the  quantitj-  of  the  voice  and 
giA'^e  the  reader  a  command  over  it  by  which  he  can  readily 
adapt  it  to  the  requisites  of  reading  or  speaking. 

In  case  of  weakness  of  voice,  arising  from  ill  health  or  lack 
of  i)hysical  strength,  a  course  of  gymnastics  is  recommended. 
The  weak  voices  with  which  many  clergA-men  are  troubled, 
coidd  be  cured  on  the  base  ball  ground  or  in  the  gymnasium 
Theological  students,  or  those  preparing  for  public  speaking, 
should  take  special  pains  to  secure  a  vigorous  constitution. 
Many  a  sermon  could  be  rendered  more  eloquent  and  effective 
in  this  wu}',  and  many  a  case  of  bronchitis  avoided. 


18-i  METHODS   OF   TEACHING. 

J'nndple. — Determine  the  standard  force  by  the  general  spirit 
of  the  piece.  If  the  general  spirit  is  unemotional,  the  standard 
force  is  moderate ;  if  the  general  spirit  is  bold,  noble,  dignified, 
etc.,  the  standard  force  is  loud  ;  if  the  general  spirit  is  grave, 
subdued,  pathetic,  etc.,  the  standard  force  is  soft.  The  pupil  who 
grasps  this  principle  and  applies  it  intelligently,  will  find  it  of 
great  value  in  reading. 

Correct  Errors. — Some  pupils  read  too  softly  or  with  too  little 
force.  This  is  often  the  case  with  young  ladies.  The  admiration 
of  the  "  low  voice  in  woman "  is  carried  to  such  an  extent  with 
many,  that  it  is  regarded  as  unladylike  to  read  in  public  so  as  to 
be  understood.  It  is  an  error,  however,  and  one  that  should  be 
corrected. 

To  correct  the  error  of  reading  too  softlj'-,  the  teacher  must 
notice  its  cause.  Reading  too  softly  is  sometimes  the  result 
of  a  weak  voice,  sometimes  of  timidity,  sometimes  it  is  merely 
an  affectation,  and  sometimes  an  unconscious  habit.  Correct 
the  first  by  strengthening  the  voice,  the  second  by  aiding  the 
pupil  to  acquire  confidence,  the  third  by  a  little  judicious  rid- 
icule, and  the  fourth  by  showing  the  pupil  the  defect  and 
inducing  him  to  overcome  it.  A  pupil  who  reads  too  softly 
may  be  placed  at  a  distance  from  the  teacher  in  reading. 
Such  pupils  may  read  dialogues,  standing  on  opposite  sides 
of  the  school-room,  or  at  some  convenient  distance  from  each 
other. 

Some  pupils  read  too  loud.  Boys  often  make  this  mistake. 
Loud  reading  was  formerly  considered  the  best  reading ;  and 
boys  would  read  almost  as  loud  as  they  could  shout.  We  can 
correct  this  error  by  showing  them  how  unnatural  and  inap- 
propriate it  is,  and  thus  lead  them  to  a  natural  method  of 
expression. 

Most  pupils  do  not  adapt  the  force  to  the  sentiment.  This 
arises  from  the  fact  that  they  do  not  understand  that  to  read 
anything  is  to  express  it  naturall}'.  This  error  needs  the 
teacher's  most  careful  attention.     The  pupil  must  be  led  to 


TEACHING  UEADIXG  OR  ELOCUTION.        185 

see  that  reading  is  natural  oral  expression,  and  that  the  force 
of  the  voice  must  be  adapted  to  the  sentiment  expressed. 

Emphasis. — Emphasis  is  particular  force  applied  to  one  or 
more  words  of  a  sentence.  Its  object  is  to  give  prominence 
and  distinction  to  the  important  ideas.  It  brings  out  the 
meaning  of  an  author,  makes  his  thoughts  and  sentiments  im- 
pressive, and  gives  beaut\-  to  expression  as  the  play  of  light 
and  shade  does  to  a  picture.  A  true  emphasis  keeps  the 
attention  of  the  listener  in  active  s^-mpathj-  with  the  thoughts 
of  the  speaker,  gives  full  effect  to  all  he  utters,  and  makes  a 
leep  and  lasting  impression  on  the  memorj'. 

There  are  two  kinds  of  emphasis;  Absolute  and  Antithetic. 
Absolute  Emphasis  is  that  which  is  applied  to  the  prominent 
ideas  of  a  sentence  without  an}-  particular  comparison  with 
other  ideas.  Antithetic  Emphasis  is  that  which  is  used  in 
contrasting  ideas;  as,  "I  said  an  elder  soldier,  not  a  better." 

Hoiv  Teach. — We  teach  Emphasis  by  means  of  Exercises, 
Imitation,  Principle,  and  Correcting  Errors. 

Exercises,  etc. — For  Exercises,  drill  the  pupils  on  well 
selected  sentences  containing  emphatic  words.  Dialogues  will 
be  found  most  suitable  for  young  pupils.  Repeating  the  ele- 
mentary sounds,  emphasizing  at  intervals,  is  a  good  drill 
exercise.  The  teacher  should  also  read  for  the  pupils,  placing 
the  emphasis  correctly,  and  require  the  pupils  to  imitate  him. 
Some  of  the  chapters  in  the  Bible,  as  that  of  the  Prodigal 
Son,  so  often  incorrecth'  read,  might  be  selected  as  an  example. 

Principle — Xo  specific  rule  can  be  given  for  emphasis ;  it  is 
a  matter  of  judgment  and  taste.  The  principle  of  Prof.  Bailey 
will  be  of  great  advantage  in  applying  emphasis.  This  prin- 
ciple is  closely  related  to  that  of  Force,  and,  as  he  gives  it,  is 
a  part  of  the  former.  It  is  as  follows:  Having  determined  the 
standard  force  for  the  unemphatic  ideas,  give  more  force  to 
the  emphatic  ideas  according  to  their  relative  importance. 

Correct  Errors. — The  teacher  should  constantly  watch  and 
correct  the  errors  of  pupils  with  respect  to  emphasis.     The 


18G  METHODS    OF    TEACHING. 

most  common  errors  are  those  of  incorrect  and  random  em 
])hasis.  Sometimes  the  emphasis  is  wrong  because  the  pupil 
mistakes  the  sense ;  this  is  corrected  by  calling  attention  to 
the  important  word.  More  freqnenti}' ,  the  emphasis  is  api)lied 
at  random,  without  any  thought  as  to  the  prominent  ideas. 
This  error  is  often  heard  in  the  reading  of  the  Bible  and  sacred 
hymns.  It  ma}-  be  corrected  by  calling  attention  to  the 
proper  use  of  emphasis,  and  the  reader's  disregard  of  it. 

A  very  common  fault  in  emphasis  is  the  use  of  the  circum- 
flex upon  the  emphatic  word  instead  of  the  slide,  as  will  be 
subsequently  explained.  The  faulty  emphasis  of  the  circum- 
flex can  be  removed  b}-  drill  on  appropriate  examples,  and  by 
expedients  adapted  to  individual  cases.  Another  fault,  often 
met  with,  is  that  of  stiflf  and  excessive  emphasis,  which  can 
be  remoA'ed  by  practice,  the  study  of  good  models,  and  the 
culture  of  taste. 

Stress. — Stress  is  force  applied  to  particular  parts  of  mono- 
syllabic words  or  s^dlables.  It  is  an  unequal  distribution  of 
force  on  a  S3'llable,  and  gives  variety  in  the  expression  of  a 
single  word,  as  emphasis  does  in  the  expression  of  a  sentence. 
There  are  five  kinds  of  stress;  Radical,  Vanishing,  Median, 
Compound,  and  TJtorough. 

Radical  Stress  is  force  applied  to  the  first  part  of  a  mono- 
syllabic word  or  of  a  syllable.  It  may  be  illustrated  In-  pro- 
nouncing the  words  eat,  out,  etc.  It  is  used  in  expressing 
anger,  command,  positive  assertion,  and  in  energetic  senti- 
ments of  all  kinds.  By  it  animals  are  awed  into  submission, 
and  audiences  are  often  startled,  thrilled,  and  swayed. 

Median  Stress  is  force  applied  to  the  middle  of  the  word 
or  syllable;  as  ma^-  be  heard  in  pronouncing  gold,  fa?-,  leap, 
etc.  It  is  used  in  expressing  dignity,  grandeur,  solemnity, 
supplication,  plaintiveness,  etc.  Median  Stress  gives  beauty 
and  expression  to  delivery.  It  is  the  natural  utterance  of 
thoughtful  sentiment,  and  the  swell  is  more  or  less  prolonged 
as  the  feeling  is  moderate,  or  deep  and  full,  lofty  and  sublime 


TEACHIXG  READING  OR  ELOCUTION.        187 

It  gives  music  to  poetry,  the  spirit  of  devotion  to  sacred  coin- 
position,  and  the  touch  of  eloquence  to  orator3-. 

Vanishing  Stress  is  force  ap{)lied  to  the  latter  part  of  a 
word  or  syllable ;  as  may  be  illustrated  in  pronouncing  hell^ 
low,  ring,  etc.  It  is  the  expression  of  intense  feeling  deferred 
ind  accumulated  upon  the  latter  part  of  a  word,  as  a  child 
says,  /  iconH,  I  shatiH.  This  stress  is  used  in  expressing 
earnest  purpose,  determination,  stern  rebuke,  contempt,  aston- 
ishment, horror,  etc.  It  is  not  so  much  an  element  of  dignity 
as  the  median  stress,  yet  it  is  an  essential  condition  of  hi<rh- 
wrought  feeling  and  impassioned  utterance.  Without  vanish- 
ing stress,  oratory  would  often  lose  its  manly  energy  of  deter- 
mined will,  and  high-wrought  resolution  would  fail  of  expres- 
sion ;  while  for  the  natural  utterance  of  the  elevated  emotion 
and  extreme  passion  of  lyric  and  dramatic  poetry,  it  is  indis- 
pensable. 

Compound  Stress  is  a  combination  of  the  radical  and  van- 
ishing stress.  It  is  force  applied  on  the  first  and  last  part  of 
a  word,  as  may  be  illustrated  in  the  sarcastic  utterance  of  the 
word  yes.  Compound  Stress  is  used  in  exi)ressing  surprise, 
sarcasm,  in  Irish  lu-ogue,  in  snap})ish  sentiments,  etc.  It  is 
not  an  agreeable  form  of  stress,  and  should  be  used  o\\\y  on 
those  rare  occasions  which  especially  demand  it.  , 

Thorough  Stress  is  stress  running  through  the  entire  word 
or  syllable.  It  is  used  in  expressing  command,  denunciation, 
bravado,  and  in  exaggerated  and  mock  heroic  sentiment. 
When  applied  to  continuous  speech,  it  destroys  the  grace  and 
delicacy  of  utterance  and  becomes  a  sign  of  rudeness  and  vul- 
garity. Judiciously  employed,  it  is  often  a  powerful  weapon 
of  oratory  ;  but  when  indiscrlminatel}^  used  it  becomes  more 
ranting,  and  excites  feelings  of  ridicule  and  disgust. 

How  Teach — Pupils  should  be  drilled  first  on  individual 
words  until  they  can  give  them  with  the  required  stress,  and 
then  upon  appropriate  pieces  requiring  ditferent  degrees  ot 
stress.     Repeatiiig  the  elementary  sounds  with  varied  stress 


188  METHODS    OF    TEACHING. 

affords  an  excellent  exercise.  The  teacher  should  also  pre 
sent  proper  examples  of  stress  for  the  pupils  to  imitate.  In 
order  to  establish  a  principle,  Bailey  includes  all  varieties  of 
stress  under  two  heads, — Smooth  and  Abrupt.  His  principle 
is  as  follows  :  All  pure  and  beautiful  ideas  should  have  smooth 
stress  ;  all  abrupt  ideas  should  have  abrupt  stress.  The  nat- 
ural language  of  stress  which  we  have  given  in  discussing  each 
kind  of  stress  will  be  a  better  guide  in  its  use,  however,  than 
this  principle. 

Slur. — Slur  is  a  smooth,  subdued,  gliding  movement  of  the 
voice  applied  to  the  less  important  parts  of  a  discourse.  It  is 
generally  used  in  what  are  called  parenthetic  passages. 

We  teach  slur  by  drilling  the  pupil  in  suitable  exercises,  by 
presenting  good  models  for  his  imitation,  and  by  correcting 
his  errors.  No  principle  can  be  given  which  will  be  of  much 
advantage  to  the  learner, 

II.  Compass. — Compass  has  reference  to  the  highness  or 
lowness  of  the  voice  in  reading  or  speaking.  In  speaking  or 
singing,  the  voice  moves  between  certain  limits,  above  or 
below  which  it  cannot  utter  sounds.  The  range  included 
between  these  limits  is  known  as  the  compass  of  the  voice. 

In  singing,  the  voice  moves  gradually  up  or  down  a  series 
of  eio-ht  sounds  called  the  Scale.  The  distance  between  any 
two  points  in  the  scale  is  called  an  Interval.  The  distance 
between  any  two  successive  sounds  of  the  scale  is  called  a 
second ;  the  distance  between  the  3d  and  4th  and  7th  and  8th, 
being  half  as  large  as  the  other  intervals,  are  called  viinor 
seconds,  while  the  others  are  called  major  seconds.  The  dis- 
tance from  one  to  three  of  the  scale  is  called  a  third,  from  one 
to  four  a/o«?'</i,  etc.,  and  from  one  to  eight  an  octave.  A 
third  which  consists  of  two  major  seconds,  is  called  a  major 
third  ;  a  third  of  one  major  and  one  viinor  second,  is  called  a 
minor  third. 

The  voice  may  pass  directly  from  one  note  of  the  scale  to 
another,  as  in  singing  ;  or  it  may  slide  from  one  degree  to 


TEACHING    READINQ    OR   ELOCUTION.  189 

another,  as  in  speaking.  The  former  is  called  a  discrete  mter- 
val ;  the  latter  a  concrete  interval.  In  tne  concrete  interval, 
the  voice  rises  concretely  through  the  different  intervals,  as  in 
sliding  the  finger  on  a  violin  string.  The  discrete  interval 
steps,  as  it  were,  from  one  tone  to  another,  like  the  tones  of 
the  organ.  The  former,  figurativel}^  speaking,  is  a  rising  or 
falling  stream  of  voice  ;  the  latter  is  a  voiceless  space. 

The  first  sound  of  the  scale  is  called  the  Key-note.  The  pitch 
on  which  a  syllable  or  word  begins,  is  called  its  Radical  Fitch; 
the  point  at  which  the  voice  arrives  by  a  concrete  or  discrete 
movement,  is  called  its  Concrete  or  Discrete  Pitch,  etc.  The 
subject  of  Compass  embraces  three  things ;  Key-note,  Slides, 
and  3Telody. 

Key-Note. — Ke^^-Note  in  elocution  is  the  standard  pitch  ot 
the  voice  used  in  reading  and  speaking.  It  is  of  three  degrees ; 
High,  Low,  and  Medium.  These  are  not  absolute  but  relative 
distinctions  of  pitch.  Different  voices  differ  naturall}^  in  pitch, 
and  what  is  medium  to  one  voice,  may  be  high  or  low  to  an- 
other; and  the  medium  pitch  of  any  one  voice  will  range 
through  several  notes. 

Voices  are  of  two  general  classes  with  respect  to  pitch ; 
men's  and  women's  voices.  These  differ  in  pitch  one  octave, 
women's  voices  being  an  octave  higher  than  men's  voices. 
Women's  voices  are  of  two  general  classes  ;  Soprano,  a  high 
female  voice,  and  Alto,  a  low  female  voice.  There  is  also  a 
voice,  sometimes  met  with, between  these  tAvo, called  Contralto. 
The  soprano  is  the  finest  voice  for  singing;  but  the  alto  and 
contralto  voices  are  usually  the  most  effective  in  reading. 

Men's  voices  are  also  of  two  general  classes;  Tenor  and 
Base.  Tenor  is  a  high  male  voice;  Base  is  a  low,  deep,  male 
voice.  There  is  also  a  voice  intermediate  between  these,  called 
Baritone.  The  base  voice  is  the  most  impressive  in  reading 
and  speaking,  and  is  especially  adapted  to  solemn  and  grave 
deliverv,  as  in  reading  the  church  service,  etc.  The  tenor  is 
capable  of  more  variety,  and,  while  less  impressive  than  the 


190  METHODS    OF   TEACHIXG. 

l)iise  voice,  is  less  tiresome  to  tlie  listener.  The  bniitoiie  is 
cf'i'ii  less  musical  than  either  of  the  others,  and  less  servicea- 
l;Ie  eitiier  in  veaclinii:  or  speaking;  though  a  rich  and  llexible 
liaiitone  is  the  best  of  all  voices  for  orator}-. 

Ilotr  Teach. — A  pupil  should  be  drilled  on  exercises  to 
give  liim  complete  master}'  over  the  pitch  of  his  voice.  First, 
he  should  practice  singing  the  musical  scale.  Second,  lie 
siiould  be  rcfpiired  to  give  the  elementary  sounds  on  difterent 
degrees  of  the  scale,  beginning  at  a  low  pitch  and  ascending 
gvadunlly  as  high  as  he  can  speak  with  ease,  and  then  gradu- 
all}-  descending  to  the  lowest  pitch.  Third,  he  should  be 
rcipiired  to  repeat  sentences  on  different  degrees  of  the  scale, 
and  to  read  selections  which  require  variety  of  pitch.  Such  a 
drill  will  enrich  the  voice  and  give  him  complete  command 
over  its  pitch  in  reading  or  speaking. 

I'rinciple. — Pupils  should  be  led  to  see  the  relation  of  the 
ditferent  degrees  of  i)itch  to  the  ditierent  varieties  of  senti- 
ment. There  is  a  natural  relation  between  the  pitch  of  the 
voice  antl  the  emotions  of  the  heart.  Deep  feeling  requires 
low  tones  ;  joyful  and  elevated  feeling  requires  a  higher  tfuie 
of  voice;  and  sorrow  and  pity,  thougii  requiring  soft  force, 
are  also  expressed  by  the  higher  notes  of  the  scale.  All  ordi- 
nary and  moderate  emotions  incline  to  the  middle  range  of 
the  scale. 

The  general  principle  to  guide  in  the  adaptation  of  the  pitch 
of  the  voice  to  the  sentiment  ma}'  be  expressed  as  follows : 
Determine  the  standard  pitch  by  the  general  spirit  of  the 
piece ;  if  the  general  spirit  is  unemotional,  the  standard  pitch 
is  medium ;  if  the  general  spirit  is  animated,  joyous,  or 
pathetic,  the  standard  pitch  is  high  ;  if  the  general  spirit  is 
noble,  grave,  dignified,  etc.,  the  standard  pitch  is  low. 

Correct  Errors. — There  are  several  classes  of  errors  in  re- 
gard to  pitch  which  require  to  be  corrected.  ]\Lai}-  pupils 
pitch  their  voices  too  high  in  reading  and  reciting.  This  is 
especially  the  case  with  young  lads  of  a  joyous  and  lively  tem- 


TEACHING    READIXO    OR    ELOCUTION.  191 

pcraracnt.  It  is  also  ti  common  f:iult  of  teachers  in  ex|)]aiiiiiuj 
to  their  pupils,  in  reading  problems  in  arithmetic,  etc.  Mauv 
public  speakers  speak  in  too  high  a  key,  and  too  many  per 
sons  do  so  in  ordinary  conversation.  A  high  pitch  is  unpleas- 
ant to  the  cultivated  ear,  and  is  totally  inadequate  to  the  ex- 
pression of  sentiments  of  veneration,  dignity,  or  sublimity. 

A  few  pupils  pitch  their  voices  too  low,  though  the  fault  is 
somewhat  rare  in  school.  A  few  public  speakers  also  habitu- 
ally use  a  grave  and  hollow  tone  of  vuice,  and  thus  impart  a 
deep  and  sepulchral  solemnit}-  to  all  subjects  alike. 

Most  pupils  and  readers  do  not  adai^t  the  pitch  to  the  sen- 
timent, reading  all  things  with  about  the  same  degree  of  pitch. 
Falling  into  this  habit,  they  use  the  same  tone  in  all  varieties 
of  subjects,  and  read  a  notice  of  a  Sunday-school  celebration 
with  as  deep  a  solemnity  of  tone  as  thej'  would  use  in 
announcing  the  death  of  a  member  or  preaching  a  funeral 
sermon. 

Many,  again,  do  not  discriminate  between  pitch  and  force. 
Tell  them  to  read  lower,  and  the}^  read  softer,  and  perhaps 
pitch  the  voice  higher.  All  errors  should  be  corrected  with 
great  care.  The  pupil  should  be  taught  to  see  the  relation 
between  the  pitch  and  the  sentiment  to  be  expressed,  and  then 
be  required  to  adapt  the  voice  to  the  nature  of  the  piece  read 
or  recited.  Those  who  speak  habitually  too  high  may  be 
given  a  pitch  of  the  scale  to  use  as  the  kej'-note  of  a  piece. 
Some  of  the  ancient  orators  used  to  have  a  person  back  of  the 
stage  to  sound  the  ke^'-note  as  they  passed  from  one  part  of 
their  speech  to  another. 

Slides. — Slides,  or  Inflections,  are  variations  of  the  pitch 
of  the  voice  on  different  words  or  syllables  of  a  sentence.  No 
two  successive  words  or  sjdlables  of  a  sentence  are  usually 
uttered  with  the  same  pitch  of  voice  ;  and  the  pitch  of  the 
voice  in  ordinary  natural  expression  usuallv  varies  in  pro- 
nouncing each  word  and  syllaljle.  We  begin  a  word  with  a 
certain  pitch  and  end  it  in  either  a  lower  or  a  higher  key.     In 


192  METHODS    OF    TEACHING. 

natural  expression,  the  voice  moves  concretely  on  words  and 
syllables,  through  the  interval  from  one  degree  of  pitch  to 
another.     Such  variations  of  pitch  are  called  Slides. 

Slides  are  of  three  ditferent  kinds ;  Rising  Slides,  Falling 
Slides,  and  the  Circumflex.  The  Rising  Slide  is  an  upward 
slide  of  the  voice  ;  it  is  often  indicated  by  the  acute  accent 
(').  The  Falling  Slide  is  a  downward  slide  of  the  voice  ;  it  is 
often  indicated  by  the  grave  accent  (').  The  rising  inflection 
denotes  hesitation  or  incompleteness  of  expression  ;  the  falling 
inflection  expresses  decision  and  completeness  of  expression. 

The  Circumflex  is  a  imion  of  the  rising  and  falling  inflection. 
It  is  called  Direct  when  the  first  interval  ascends  ;  Inverted 
when  the  first  movement  descends.  It  is  said  to  be  Equal 
when  the  two  slides  arc  of  the  same  degree,  and  Unequal  when 
they  are  of  ditterent  degrees.  It  is  called  Single  when  two 
intervals  only  are  joined,  as  (V);  and  Double,  when  there  are 
more  than  two,  as  (w). 

The  use  of  slides  and  inflections  is  to  give  variety,  beauty, 
and  significance  to  speech.  In  connection  with  force,  they 
constitute  emphasis,  and  thus  give  prominence  to  the  emphatic 
ideas.  In  emphasis,  it  will  be  noticed,  we  have  not  only 
more  force,  but  longer  slides.  Slides  give  variety  to  speech, 
for  without  it  our  reading  would  be  monotonous  and  weari- 
some. They  add  the  charm  of  melod}'  or  music  to  our  utter- 
ances, and  thus  render  our  reading  or  speaking  more  pleasing 
to  the  ear. 

Slides  may  be  of  various  degrees.  Thus,  the  voice  may 
vary  a  second,  a  third,  a  fourth,  etc.,  as  far  as  the  octave. 
The  Second  is  the  rise  or  fall  of  the  voice  between  any  two 
degrees  of  the  scale.  Seconds  are  both  major  and  minor,  as 
previously  explained.  The  term  second,  in  reading,  is  usually 
applied  to  the  major  second.  Thirds  are  also  both  major,  as 
from  the  first  to  the  third  of  the  scale,  and  minor,  as  from  the 
sixth  to  the  eighth  of  the  scale. 

The  Second  is  the  basis  of  correct  and  agreeable  elocution 


TEACHING  READING  OR  ELOCUTION.  193 

It  is  raore  used  than  any  other  interval,  being  appropriate  to 
those  parts  of  discourse  which  convey  the  plain  thoughts  of 
the  speaker  rather  than  those  which  express  passion  an<1  ex- 
citement. The  second  is  the  least  obtrusive  interval  of  the 
scale,  and  is  the  simple  sign  of  the  unexcited  sentiment  of 
wisdom  and  truth.  "  The  simple  rise  and  fall  of  the  second," 
says  Dr.  Rush,  "  and  perhaps  its  wave,  when  used  for  plain 
narration,  or  for  the  mere  statement  of  an  unexcited  idea,  is 
the  only  intonated  voice  of  man  that  does  not  spring  from  a 
jjassionate  or  an  earnest  condition  of  his  mind." 

The  slide  of  the  Third  is  used  for  more  earnest  and  ani- 
mated discourse  than  the  second.  The  Downward  Third  ex- 
presses considerable  feeling,  though  somewhat  subdued  and 
dignified.  In  simple  narrative,  it  is  often  used  with  the  sec- 
ond, in  giving  emphasis  to  the  prominent  words.  The  Rising 
Third  is  used  in  asking  questions,  and  also  for  emphasis.  It 
is  tlie  sign  of  interrogation  in  its  most  moderate  form,  and 
denotes  but  little  earnestness  or  animation  in  the  inquiry 
The  Minor  Third  is  used  in  the  emphatic  words  of  pathetic 
utterance;  as  "  Little  Nell  was  dead.     She  died  last  night." 

The  slide  of  the  Fifth  is  used  for  very  earnest  and  animated 
discourse.  The  Downward  Fifth  is  employed  in  expressing 
surprise,  admiration,  and  dignified  command.  It  indicates 
strong  emotion,  but  under  the  influence  of  the  will  and  with- 
out the  excitement  of  passion.  The  Rising  Fifth  is  used  for 
earnest  interrogation,  or  for  the  emphatic  expression  of  in- 
quiry or  doubt.  Very  few  inquiries  need  a  longer  slide  than 
the  fifth.  Any  larger  interval,  on  account  of  the  difficulty  of 
managing  the  voice,  loses  instead  of  gaining  in  force  of  ex 
pression. 

The  Octave  Slide  is  used  for  the  most  earnest  and  animated 
discourse.  The  Falling  Octave  expresses  the  highest  degree 
of  admiration  or  astonishment,  and  the  most  positive  com- 
mand. Very  few  pieces  of  composition  require  the  octave, 
and  in  all  ordinary-  utterances  it  would  seem  exaggerated  and 


19i  METHODS   OF   TEACHING. 

inappropriate.  The  Rising  Octave  expresses  the  most  forci- 
ble degree  of  interrogation  and  of  emphasis  on  a  rising  inter- 
val. It  is  appropi'iate  for  the  expression  of  contempt,  mirth, 
raillery,  and  of  peevish  or  indignant  argument.  When  cm- 
ployed  in  ordinary  or  moderatel}'  earnest  discourse,  it  be- 
comes ludicrous.  Slides  on  the  other  degrees  of  the  scale  are 
so  seldom  used  that  they  are  not  described. 

How  Teach. — Pupils  should  be  drilled  on  the  slides  until 
they  can  give  them  readily  of  any  kind  and  degr^.  The 
vocals  of  the  list  of  the  elementary  sounds,  may  be  used  -for 
this  i)urpose,  and  also  well  selected  sentences.  Some  good 
teachers  use  the  violin  in  training  the  ear  and  voice  in  the 
matter  of  slides.  The  teacher,  of  course,  should  be  able  to 
irive  them  well  himself  as  a  model  for  the  imitation  of  his 
pupils. 

In  order  to  apply  a  principle  with  respect  to  slides,  all  ideas 
may  be  divided  into  two  classes;  positive  ideas  and  negative 
ideas.  Positive  ideas  are  those  which  are  used  in  alllrming, 
denying,  or  making  an  inciuiry  in  a  positive  form.  Negative 
ideas  are  those  which  do  not  affirm  or  deny  positively,  wliich 
are  in  contrast  with  positive  ideas,  or  which  are  used  in  ask- 
ing a  direct  question.  The  former  denote  something  com- 
pleted and  definitely  laid  down  ;  the  latter  indicate  something 
incomplete,  unfinished,  or  held  up  for  further  consideration. 
Such  ideas  have  been  regarded  as  direct,  while  those  which 
are  neither  i)o.sitive  or  negative  have  been  called  "crooked 
ideas,"  as  those  of  jest,  sarcasm,  irony,  etc. 

The  general  principle  is, — All  positive  ideas  should  have 
the  falling  slides;  all  negative  ideas  should  have  rising  slides; 
and  all  crooked  ideas  should  have  the  circumflex  slides. 
Thus,  all  assertions  or  denials  or  questions  containing  a 
spirit  of  assertion  or  denial  should  have  downward  slides; 
all  questions  desiring  an  answer  should  have  rising  slides; 
wliile  irony,  ridicule,  insinuation,  etc.,  require  the  circumflex 
slide. 


i 


TEACHING    READING   OR    ELOCUTION.  195 

The  degree  of  the  slide  is  determined  by  the  nature  of  the 
jentiment.  Unemotional  pieces  have  short  slides ;  bold,  dig- 
niticd  pieces  have  long  slides.  Very  pathetic  pieces  require 
minor  slides.  These  principles  govern  the  majority  of  cases; 
but  it  should  be  remembered  that  the  slide  is  largely  subject 
to  the  demands  of  variety,  melody,  and  to  the  relations  of  the 
different  parts  of  the  sentiment  expressed. 

Melody. — Melody  is  a  series  of  simple  sounds  so  varied  in 
pitch  as  to  produce  a  pleasing  effect  upon  the  ear.  Melody  in 
reading  is  an  agreeable  variation  of  the  pitch  of  the  voice  on 
and  between  the  successive  words  and  syllables  of  a  sen- 
tence. It  will  be  noticed  that  in  natural  expression  there  is 
a  difference  of  pitch  between  words  and  syllables  as  well  as  a 
variation  of  pitch  on  them.  The  pitch  of  voice  at  which  any 
word  begins  is  a  little  lower  or  higher  than  the  pitch  at  which 
the  previous  word  ends.  The  term  melody  includes  this  varia 
tion,  and  is  also  generally  used  to  embrace  the  entire  variation 
of  the  pitch  of  the  voice  in  reading  or  speaking. 

The  object  of  melody  is  to  give  beaut}'  and  variety  to  read- 
ing. It  is  the  musical  element  of  speech,  and  imparts  a  grace 
and  charm  to  utterance,  preventing  monotony,  and  giving 
delight  to  the  ear.  Its  absence  leaves  the  wearisome  effect  of 
the  unvarying  monotone.  It  also  enables  the  voice  to  rise  or 
fall  gradually  on  the  unemphatic  words,  that  it  may  have  an 
opportunity  for  longer  slides  on  the  emphatic  words. 

There  are  two  distinct  kinds  of  melody;  Diatonic  and  Semi- 
tonic.  Diatonic  melody  is  a  variation  of  a  major  second  on 
and  between  successive  words  and  S3'llables.  Semitonic  mel- 
ody is  a  variation  of  a  minor  second  on  and  between  suc- 
cessive words  and  syllables.  The  absence  of  melody  pro- 
duces Monotone.  Monotone  is  a  sameness  of  pitch  on  and 
bctAveen  successive  words  and  syllables. 

Diatonic  melody  is  used  for  the  expression  of  all  sentiment 
except  the  very  pathetic  or  sublime.  It  indicates  manly  con- 
fidence and  the  self-reliance  of  truth.     Semitonic  melody  is 


196  METHODS   OF   TEACHING. 

used  in  ver}'  pathetic  dis^v^urse.  It  expresses  complaint,  pity, 
grief,  plaintive  supplication,  and  the  like.  A  misplaced  use 
of  the  semitone  leads  lo  whining.  It  is  difficult  to  crive  semi- 
tonic  melody  with  artistic  effect;  and  when  overdone,  it 
awakens  fcelins;s  of  the  ludicrous. 

The  Monotone  is  used  in  expressing  grandeur  of  thought 
and  sublimit}'  of  feeling.  It  is  used  in  expressing  fear,  vast- 
ness,  majesty,  power,  etc.,  sentiments  wliich  seem  to  partially 
obstruct  or  overawe  the  powers  of  utterance.  The  ell'eet  pro- 
dued  by  it  is  deep  and  impressive.  AVhen  properly  em- 
ployed, the  reading  will  be  characterized  by  a  solenmity, 
dignity,  and  grandeur,  entirely  in  harmony  with  the  senti- 
ments expressed. 

Cadence. — Melody  gives  rise  to  what  is  called  the  Cadence. 
Cadence  is  the  closing  tone  of  a  sentence.  The  completion  of 
a  thought  is  expressed,  not  only  by  the  long  pause  which  takes 
place  at  the  end  of  a  sentence,  but  usually  b}'  a  falling  of  the 
voice  on  the  closing  words  to  a  lower  pitch  than  that  which 
prevailed  in  the  body  of  the  sentence.  This  closing  descent 
in  the  tone  is  used  to  prevent  the  abruptness  and  irregularity 
of  sound  which  would  be  produced  by  continuing  the  prevail- 
ing pitch  to  the  close  of  the  sentence.  It  is  a  prophecy  of  a 
close,  prepares  the  mind  for  it,  and  thus  avoids  that  surprise 
which  would  be  at  variance  with  both  harmony  and  meaning. 

The  note  to  which  the  cadence  falls  and  the  space  through 
which  it  descends,  are  dependent  on  the  emotion  which  is  to 
be  uttered,  or  on  the  length  or  complication  of  the  sentence. 
In  strong  emotion,  the  cadence  is  often  both  abrupt  and  low; 
as,  "  Let  us  do,  or  die."  In  gentle  emotion,  the  cadence  is 
gradual  and  moderate  ;  as,  "  How  sweet  the  moonlight  sleeps 
upon  this  bank."  In  short  sentences,  where  the  emotion  is 
slight,  the  fall  is  slight;  as,  "  Night  brings  out  stars, as  sorrow 
shows  us  truth."  In  long  sentences,  the  fall  is  more  obvious 
and  begins  further  from  the  close. 

Uow  Teach. — Pupils  should  be  drilled  on  the  elementary 


TEACHIXQ   READING    OR   ELOCUTION'.  197 

sounds  and  suitable  exercises  until  they  are  familiar  with 
melody.  The  teacher  should  be  skilled  iu  it  liimself,  that  he 
may  present  suitable  models  for  imitation.  The  i)rincii)le  is 
indicated  above  in  speaking  of  the  adaptation  of  the  ditferent 
kinds  of  melody  to  the  various  kinds  of  composition. 

Principle. — We  determine  the  melody  by  the  general  spirit 
of  the  piece  ;  all  ordinary  sentiment  requires  diatonic  melody; 
very  pathetic  sentiment  should  have  semitonic  melody  ;  and 
very  sublime  discourse  may  be  given  with  the  monotone. 
To  allow  for  emphasis  we  should  let  the  voice  ascend  on  the 
unemphatic  parts  of  the  discourse  so  that  we  may  have  room 
to  slide  downward  on  the  emphatic  ideas. 

Correct  Errors. — Some  of  the  more  common  faults  of 
cadence  are  the  following:  Delaying  the  fall  of  the  voice  till 
the  last  word  or  words  of  the  sentence,  and  dropping  at  once 
from  a  preceding  uniform  tone.  This  is  a  common  fault  with 
children,  or  with  pupils  reading  what  the}'  do  not  understand. 

Falling  very  low  in  the  closing  phrase.  This  fault  is  con- 
tracted b}'  reading  onl^-  grave  and  formal  selections,  and  is 
frequently  heard  in  the  pulpit,  and  from  young  people  who 
imitate  the  ministerial  style. 

A  gradual  sliding  downward  from  the  beginning  of  the  sen- 
tence. Some  speakers  or  readers  commence  a  sentence  on  a 
high  note  with  full  force,  and  gradually  lower  the  pitch  and 
diminish  the  force  in  the  progress?  of  the  sentence,  until  the 
tone  has  nearly  died  awa\'  at  its  close.  This  fault  is  often 
heard  in  the  pulpit.  The  pupil's  attention  should  be  called  to 
an}'  one  of  these  faults  to  which  he  is  subject,  and  care  be 
taken  to  correct  the  error. 

III.  Time. — Time  has  reference  to  the  fastness  or  slowness 
in  reading  or  speaking.  It  includes  two  things  ;  Movement 
and  Pauses. 

Movement. — Movement  is  the  rate  with  which  we  read  or 
speak.  There  are  three  degrees  of  movement ;  Fast,  Slow, 
and  Moderate.     These  of  course  express  relative  rather  than 


198  METHODS   OF   TEACHING, 

absolute  desrrees  of  time.     Some  writers  also  make  the  dis- 
tinction  of  Yery  Fast  and  Yery  Slow. 

Moderate  Rate  is  the  ordinar}-  rate  used  in  speaking  oi 
reading.  It  denotes  self-possession,  a  complete  command  of 
one's  powers,  and  an  unexcited  state  of  feeling.  It  is  suitable 
to  unimpassioned  language,  and  is  emplo3-ed  in  narrations 
descriptions,  and  didactic  composition. 

Fast  or  Rapid  Movement  is  that  which  is  quicker  than  mod 
erate  rate.  It  is  characteristic  of  gay,  exhilarated,  and  joyful 
feelings  ;  and  indicates  some  excitement  of  mind.  It  is  used 
in  giving  utterance  to  all  playful,  humorous,  and  mirthful  sen- 
timents, in  excited  argument,  and  also  in  expressing  indigna- 
tion and  fear.  Very  quick  or  rapid  movement  is  expressive 
of  haste,  alarm,  confusion,  and  extreme  terror. 

Slow  Movement  is  a  slower  rate  than  moderate.  It  is  sug- 
gestive of  repose,  grandeur,  majestj',  vastness,  power,  and 
splendor.  It  is  used  in  expressing  the  deeper  emotions  of 
grief,  reverence,  grandeur,  sublimity,  etc.,  and  gives  dignity 
and  impressiveness  to  discourse.  Very  slow  movement  is 
emploj'ed  in  expressing  the  very  strongest  and  deepest  emo- 
tions; as,  horror,  awe,  profound  reverence,  solemnit}-,  adora- 
tion, etc.  It  is  especially  suitable  to  man}-  parts  of  the  Bible, 
and  to  the  discussion  of  man}'  sacred  themes. 

Hoiv  Teach. — Drill  pupils  on  suitable  exercises,  so  that 
the}-  may  be  able  to  have  a  complete  command  over  their 
voices  with  respect  to  rate.  Like  a  good  musician,  they 
should  be  able  to  read  rapidly  or  slowly  at  pleasure.  They 
must  be  led  to  see  that  in  order  to  read  slowly,  the  voice  is 
to  be  prolonged  on  the  vowel  sounds  of  words,  and  the}' 
should  be  drilled  until  they  can  adopt  any  rate  at  pleasure. 
The  importance  of  such  drill  appears  in  the  fact  that  it  is 
more  difficult  to  command  the  rate  of  reading  than  one  would 
naturally  suppose.  The  teacher,  of  course,  should  be  able  U 
present  suitable  models  for  imitation. 

Principle. — The   principle  for   rate  is  as  follows:    Deter 


TEACHING    READING    OR    ELOCUTION.  199 

mine  the  standard  rate  by  the  general  spirit  of  the  piece.  If 
the  general  sjjirit  is  nneraotional.  the  standard  rate  is  moder- 
ate;  if  the  general  spirit  is  animated,  joj'ous,  ga}',  etc.,  the 
standard  rate  is  fast;  if  the  general  spirit  is  bold,  grave,  dig- 
nified, etc.,  the  rate  is  slow.  Taking  the  standard  rate  for  the 
unempliatic  words,  give  additional  time  to  the  emphatic  ideas, 
according  to  their  relative  importance. 

Correct  Errors. — The  teaciier  mnst  also  be  carefnl  to  cor- 
rect the  errors  of  i)upils  with  respect  to  rate.  Most  pupils 
read  too  fast.  This  may  be  corrected  by  leading  them  to 
dwell  on  the  vocal  sounds  of  the  words.  With  very  young 
pupils  concert  reading  is  a  useful  exercise,  as  they  usually  I'ead 
more  slowly  when  pronouncing  the  words  togethei'.  Nearly 
all  young  s|)eakers  speak  too  ra])idly  in  debate  and  declama- 
tion, and  rapid  speaking  is  a  veiy  general  fault  of  extempor- 
aneous sjjcakers. 

A  few  pupils  read  too  slowly,  prolonging  the  words  into  a 
drawl.  •Such  must  be  drilled  to  speak  their  words  more 
quickly.  Have  them  shorten  the  vowel  sounds  of  words. 
Let  the  teacher  give  them  lively  sentences  to  read,  and  en- 
deavor to  give  vivacit}'  and  animation  to  their  style. 

Nearly  all  pupils  tail  to  adapt  the  rate  to  the  sentiment, 
reading  all  kinds  of  discourse  with  the  same  rate.  This  must 
be  corrected  by  calling  attention  to  the  relation  of  rate  to  sen- 
timent, and  l>y  unremitting  drill. 

1'auses.— Pauses  are  cessations  of  the  voice  in  reading  and 
speaking.  They  are  the  intervals  between  the  utterance  of 
word-i,  clauses,  sentences,  and  jviragraphs,  which  correspond 
with  and  mark  the  divisions  of  meaning. 

Then' are  two  kinds  of  pauses  ;  the  Grammatical  and  the 
IMietoricil.  The  (Jrammatical  Pauses  are  those  which  indicate 
the  logical  or  gramm:i,tical  relation  of  the  different  parts  of  the 
discourse ;  tlu'v  are  represented  by  the  punctuation  marks. 
Tlie  Ulictorical  Pauses  are  those  which  are  recpiired  to  bring 
out  the  sense  or  exjjress  the  sentiment  of  a  discourse;  they 


200  METHODS   OF   TEACHING. 

are  not  marked,  but  are  determined  by  the  sense  of  the  piece 
and  the  judgment  of  the  reader. 

Pauses  are  of  great  importance  in  reading  and  speaking 
They  are  required  both  for  ease  of  utterance  and  for  clear  and 
emphatic  expression.  They  are  useful  to  both  the  reader  and 
the  listener.  To  the  speaker  the  rhetorical  pause  is  necessary 
for  breathing  after  uttering  a  succession  of  sounds  embracing 
at  least  one  word  which  demands  a  great  impulse  of  the 
organs,  and  which  partiall}'  exhausts  the  suppl}-  of  breath. 

The  rhetorical  pause  is  specially  important  to  the  listener. 
A  proper  pause  at  the  end  of  a  sentence,  rests  the  mind  of  the 
hearer,  and  gives  it  time  to  dwell  a  moment  upon  the  idea  or 
sentiment  presented.  A  pause  after  an  emphatic  word  gives 
the  mind  an  opportunity  to  linger  on  the  idea  and  receive  the 
full  impression  from  it.  As  some  one  remarks,  it  gives  time 
for  the  idea  "  to  soak  in"  the  mind  of  the  hearer.  It  is  thus 
true,  in  more  senses  than  one,  thai  "  a  pause  is  more  eloquent 
than  words;"  and  that  though  "speech  may  be  silvern,  silence 
is  golden." 

How  Teach. — Pupils  should  be  drilled  in  exercises  to  ac-' 
quire  the  right  use  of  pauses.  Show  them  the  necessity  and 
use  of  the  rhetorical  pause.  Make  them  see  that  the  length 
of  the  pause  depends  on  the  sense,  and  not  on  the  punctua- 
tion. The  old  method  of  counting  one  at  a  comma,  two  at  a 
semicolon,  etc.,  is  entirely  objectionable.  Show  them  also 
the  use  of  the  emphatic  pause,  and  drill  them  in  using  it. 
Let  the  teacher  give  correct  models,  and  correct  all  errors. 

Principle. — The  length  of  the  pause  depends  on  the  nature 
of  the  discourse  spoken  or  read.  In  unemotional  composition 
the  pauses  are  moderate ;  in  energetic  and  impassioned  utter- 
ance the  pauses  are  long  in  order  to  give  impressive  emphasis; 
in  strong  and  excited  utterance  they  are  often  short  and  irreg- 
ular. Awe,  solemnity,  grandeur,  etc.,  require  long  pauses, 
both  at  the  end  of  sentences  and  for  emphasis. 

Patfse  in  Poetry. — The  measured  character  of  verse  requires 


TEACHING    READING    OR    ELOCUTION.  201 

certain  pauses  not  used  in  prose.  These  are  called  the  Poetical 
or  Harmonic  pauses.  The  Final  pause  is  a  short  pause  often 
used  at  the  end  of  a  line  to  mark  its  close.  The  Ctesural 
pause  is  that  which  is  used  to  divide  a  line  into  equal  oi-  un- 
equal parts.  The  Demi-cassural  pause  is  a  short  pause  which 
is  sometimes  used  to  divide  the  parts  of  the  line  already' 
divided  bj-  the  ctEsura.  The  rhetorical  and  ciBsural  pauses 
usuall}' coincide.  When  no  pause  is  required,  either  b}-  the 
punctuation  or  the  sentiment,  the  harmonic  pau^e  should  not 
be  observed. 

Reading  Poetry. — The  chief  faults  to  be  avoided  in  reading 
poetry  are  the  following:  1.  Too  rapid  utterance,  b}-  which  the 
effect  of  the  verse  is  lost  to  the  ear ;  2.  A  jiiain  and  dr^'^  articu- 
lation, which,  though  it  may  bring  out  the  meaning,  does  not 
indicate  the  beaut}^  of  the  sentiments  and  the  rhythm  ;  3. 
A  mechanical  observance  of  the  harmonic  pauses,  without 
regard  to  the  meaning;  4.  A  mouthing  and  chanting  tone,  pro- 
ducing the  effect  of  bombast  and  mock  solemnit}-,  5.  A  sing- 
song stjde,  as  frequently  heard  in  the  school-room. 

Poetry  should  be  read  a  little  more  slowly  than  prose,  with 
a  moderate  prolongation  of  vowel  and  liquid  sounds,  a  slight 
degree  of  musical  utterance,  and  with  an  exactness  of  time,  as 
indicated  by  the  nature  of  the  verse  and  the  emotion  ex- 
pressed. The  utterance  should  indicate  the  metre  but  should 
never  render  it  prominent. 

IV.  Quality. — Quality  of  tone  has  reference  to  the  kind  of 
voice  used  in  reading  and  speaking.  It  is  one  of  the  most  im- 
portant elements  of  vocal  expression.  The  tone  itself,  inde- 
pendent of  the  words  used,  is  expressive  of  thought  and  feel- 
ing. Tone  is  the  language  of  the  heart ;  the  soul  can  be 
thrilled  by  the  utterance  of  melodious  and  varied  sound.  A 
rich,  sweet  voice  will  hold  the  attention  of  an  audience,  even 
when  there  is  no  especial  interest  in  the  thought  expressed. 
A  pleasing  voice  will  cast  a  charm  of  feeling  and  intei'est 
around  the  dullest  composition. 


202  METHODS   OF   TEACHIXQ. 

All  the  varied  tones  which  can  be  uttered  b}'  the  human 
voice  have  been  embraced  under  six  classes;  Pure,  Orotund, 
Tremulous,  Aspirated,  Guttural,  and  Falsetto.  These  difter 
in  different  persons  in  accordance  with  the  natural  quality  of 
the  voice,  j'et  they  represent  distinct  characteristics  of  the 
voice  of  each  individual. 

Pure  Tone  is  a  pure,  clear,  round  tone  of  voice.  It  is  the 
ordinarj'  tone  of  a  good  natural  or  well-trained  voice.  All  the 
breath  is  vocalized,  and  the  tone  is  produced  by  a  very  slight 
resonance  in  the  head.  It  is  appropriate  to  all  kinds  of  dis- 
course not  strongly  emotional. 

Orotund  is  a  full,  deep,  round,  chest  tone  of  voice.  It  is 
produced  by  a  greater  resonance  in  the  head  and  chest,  and 
requires  a  depression  in  the  larj'nx,  an  opening  of  the  throat, 
extension  of  the  mouth,  and  expansion  of  the  chest.  It  is 
appropriate  to  the  expression  of  sentiments  of  dignity, 
grandeur,  etc.  It  is  emplo3'ed  in  reading  epic  and  dramatic 
poetry,  and  is  indispensable  in  oratorj'. 

Orotund  qualit}'  admits  of  three  degrees ;  Effusive,  Expul- 
sive, and  Explosive.  Effusive  Orotund  is  used  in  the  utter- 
ance of  sentiments  of  solemnity  and  pathos,  when  mingled 
with  grandeur  and  sublimit3\  It  is  also  the  appropriate  tone 
of  reverence  and  adoration. 

Expulsive  Orotund  belongs  to  earnest  and  vehement  decla- 
mation, to  impassioned  emotion,  and  to  any  sentiment  uttered 
in  the  form  of  shouting.  Explosive  Orotund  is  the  language 
of  intense  passion.  It  is  heard  when  the  violence  of  the  emo- 
tion seems  beyond  the  control  of  the  will,  as  in  a  sudden 
ecstasy  of  terror  or  anger. 

Tremulous  Tone  is  a  vibratory  tone  of  voice.  It  consists 
of  a  vibration  of  the  pitch  of  the  voice  in  the  utterance  of  a 
word.  It  is  used  in  expressing  pathetic  sentiments,  in  grief, 
pity,  sympath}",  tenderness,  etc.;  in  suppressed  excitement; 
in  the  trembling  tones  of  old  age,  and  occasionally  in  the 
exuberance  of  joy.     A  slight  tremor  often  adds  a  charm  to 


TEACHING    READING    OR   ELOCUTION.  203 

utterance,  as  the  tremula  in  singing  and  violin  plajang  does  to 
music.  It  siiould,  however,  be  used  with  discretion,  being 
careful  that  it  is  not  overdone,  when  it  savors  of  affectation. 
Dropping  in  now  and  then  unexpectedly  on  expressive  or 
tender  words,  it  produces  a  very  tine  effect. 

Aspirated  Tone  is  a  whispered  articulation,  or  a  speaking  by 
articulating  the  breath  rather  than  the  voice.  It  is  used  to 
give  increased  intensity  to  the  utterance  of  the  various  emo- 
tions. It  imparts  an  air  of  mystery  to  a  subject,  and  is  thus 
used  in  expressing  wonder,  fear,  and  in  circumstances  where 
the  voice  is  awed  into  silence.  It  is  sometimes  used  in  givino- 
utterance  to  scorn,  contempt,  rage,  etc.,  where  the  intensity 
of  feeling  seems  to  choke  or  destroy  the  power  of  vocal  utter- 
ance. 

The  Guttural  is  a  deep  throat  tone  of  voice.  It  is  a  depth 
of  utterance  so  low  as  to  pass  beyond  the  range  of  pure  tone. 
It  is  used  in  expressing  hatred,  contempt,  loathing,  etc. 

The  Falsetto  is  that  peculiar  tone  heard  in  the  higher 
degrees  of  pitch  after  the  natural  voice  breaks  or  apparently 
transcends  its  range.  It  is  used  in  the  expression  of  extreme 
surprise,  mockery,  etc.,  and  in  the  emphatic  scream  of  terror, 
pain,  etc.  The  most  common  use  of  it  is  with  men  in  imitat- 
ing female  voices. 

Hoiv  Teach — Drill  the  pupils  on  exercises  until  they  can 
readily  give  all  the  various  kinds  of  tone.  Lead  them  to  see 
the  adaptation  of  the  tone  to  the  sentiment.  Correct  all 
errors  in  respect  to  the  quality  of  the  voice.  If  there  are  any 
natural  defects  of  quality,  point  out  the  errors  and  endeavor 
to  have  the  pupils  correct  them.  Have  them  imitate  the 
teacher,  and  apply  the  principles.  The  princii)les  are  given  in 
the  statements  of  the  natural  relation  of  the  quality  to  the 
sentiment  to  be  expressed. 


204  METHODS    OF   TEACHING. 

III.  The  Physical  Element  in  Reading. 

The  Physical  Element  is  that  which  pertains  to  the  body  and 
its  members.  It  is,  as  it  were,  the  addition  of  visible  lan- 
guage to  oral  expression,  and  is  thus  used  to  give  emphasis 
and  impressiveness  to  the  spoken  words.  It  includes  Breath- 
ing, Posture,  Gesture,  and  Facial  Expression. 

I.  Bredithing. —  In  order  to  read  or  speak  well  one  m  ist 
know  how  to  breathe  correctly.  It  is  an  element  of  gv^at 
importance,  and  one  which  has  been  greatly  neglected.  Many 
public  speakers  ruin  their  voices  merely  because  they  do  not 
know  how  to  breathe.  Teachers'  voices  "  give  out"  because 
thej^  make  the  muscles  of  the  throat  do  the  work  of  the  sides 
and  waist.  Preachers  are  on  the  retired  list  with  bronchitis 
who  might  have  preached  half  a  century,  if  they  had  known 
how  to  breathe  properly.  We  present  the  following  sugges- 
tions upon  this  subject: 

Hoiv  to  Jiveaihe. — Breathe  deeply.  Some  people  breathe 
merely  with  the  upper  part  of  the  lungs.  Let  the  entire  lungs 
be  brought  into  action.  Breathe  all  the  way  down  to  the  waist. 
Let  the  diaphragm  be  lowered,  let  the  muscles  of  the  back  and 
the  sides  be  brought  into  action,  and  let  the  waist  be  enlarged, 
even  at  the  sacrifice  of  tight  clothing  and  a  false  ideal  of 
beaut3%  Such  an  exercise  will  be  of  great  value  to  weak 
lungs  as  well  as  to  weak  voices. 

Use  no  more  breath  in  speaking  than  is  needed.  Very  little 
breath  is  vocalized  in  speaking  or  reading,  as  may  be  seen  by 
holding  a  piece  of  tissue  paper  hung  by  a  silken  thread,  befoi-e 
the  mouth,  when  speaking.  The  paper  will  scarcely  move 
except  in  uttering  the  aspirates.  Let  the  breath,  therefore, 
be  used  with  economy  to  insure  ease  and  freedom  of  utterance 
There  is  no  need  of  pupils  getting  out  of  breath  in  reading  oi 
speaking,  and  the  puffing  and  blowing  of  some  speakers  is  not 
only  unnecessary  but  ridiculous,  reminding  one  of  the  spout- 
ing of  a  porpoise. 


TEACFIING    READING    OR   ELOCUTION.  205 

Be  careful  not  to  mix  the  breath  with  the  voice.  This  is  a 
fault  occasional!}'  met  with  among  3'oung  pupils,  and  is  a 
serious  error  in  delivery.  "Every  tone,"  says  Madam  Seller, 
"  requires  for  its  greatest  possible  perfection,  only  a  certain 
quantity  of  breath,  which  cannot  be  increased  or  diminished 
without  injury  to  its  strength  in  the  one  case,  and  its  agreea- 
ble sound  in  the  other."  The  use  of  too  much  breath  mars 
the  beauty  of  utterance  and  exhausts  the  reader. 

In  breathing,  the  air  should  be  inspired  thi'ough  the  nose, 
and  not  through  the  mouth.  A  speaker  who  takes  in  air 
through  his  mouth  will  find  his  throat  becoming  dry  by  the 
evaporation  of  the  mucus,  or  natural  moisture  with  which 
nature  lubricates  the  vocal  organs.  Besides,  if  there  are  any 
irritating  particles  in  the  air,  they  will  produce  an  irritation 
and  titillation  in  the  throat. 

n.  Posture. — Posture  has  reference  to  the  position  of  the 
body  and  its  members.  The  position  of  a  person  in  reading  or 
speaking  is  a  matter  that  should  not  be  overlooked.  A  person's 
appearance  before  an  audience  has  much  to  do  with  the  attention 
with  which  people  listen  to  what  he  says.  Anything  awkward, 
clownish,  or  affected  in  the  attitude,  will  naturally  prejudice  an 
audience  against  a  reader  or  speaker. 

Elements  of  Posture. — Posture  includes  the  position  of  the 
feet,  the  hands,  the  head,  and  the  body. 

The  Feet. — The  feet  should  be  placed  at  an  angle  with  each 
other,  the  weight  of  the  body  resting  on  one  foot  instead  of 
on  both.  The  foot  not  sustaining  the  bod}'  should  be  thrown 
slightly  forward  of  the  other,  in  such  a  position  that  if  drawn 
towards  the  other,  the  heel  of  it  would  come  to  the  hollow  of 
the  other.  The  foot  wliich  sustains  the  weight  should  be  so 
placed  that  a  perpendicular  let  fall  from  the  pit  of  the  neck 
would  p.iss  through  its  heel,  the  centre  of  gravity  of  the  body 
being,  fir  the  time,  in  that  line.  The  sustaining  foot  is  to  be 
planted  firmly,  the  leg  braced  but  not  contracted,  the  other 
foot  an  1  limb  being  relaxed  and   resting  for  change.      Thf 


206  METHODS   OF   TEACHIXG*. 

weight  should  be  occasionally  changed  from  one  foot  to  the 
other,  care  being  taken  that  the  transition  be  gently  and  easily 
made.  The  characteristics  of  a  good  attitude  are  thus  firm- 
ness, freedom,  simplicity,  and  grace. 

Another  position  of  the  feet  is  that  in  which  the  toes  are  on 
a  line,  the  feet  being  slightly  inclined  to  each  other,  the  toes 
turning  outward.  There  are  persons  with  some  peculiarity  of 
the  shai)e  of  the  legs  or  feet,  to  whom  this  position  is  more 
suitable  than  the  one  previously  described.  This  position  is 
usuall}'  more  becoming  to  short  than  to  tall  persons,  and  is 
especially  suitable  to  children. 

The  errors  of  position  are:  continually  changing  the  weight 
of  the  bod}'  from  one  foot  to  the  other ;  swinging  to  and 
fro  ;  jerking  the  body  forward  at  regular  intervals,  or  after 
every  emphatic  word;  crossing  the  feet  or  the  legs;  turn- 
ing in  the  toes ;  standing  with  one  foot  on  a  stool  or  chair 
round,  etc.  An  over-nicety  in  regard  to  position  that  attracts 
attention  is  also  objectionable.  Care  should  be  taken  to  avoid 
all  those  errors.  The  posture  should  be  equally  removed 
from  the  awkwardness  of  the  rustic  and  the  affectation  of  the 
dancing-master.  It  should  be  natural,  free  from  any  bad 
liabits  ;  and  will  thus  be  both  easy  and  graceful. 

Tlie  Hands. — The  hands  should  hang  naturall}'  and  easil}- 
down  at  the  side,  except  when  they  are  being  used  for  ges- 
tures. The  fingers  should  be  slightl}-  bent  and  just  touch 
each  ("ther,  and  the  thumb  should  be  parallel  to  the  fingers. 
Gentlemen  sometimes  place  one  hand  at  the  waist,  supported 
by  the  vest  or  buttoned  coat,  and  ladies  often  read  and  recite 
with  one  or  both  hands  at  the  front  of  the  waist.  These  posi- 
tions are  perhaps  not  ver}-  objectionable,  but  are  regarded  as 
less  elegant  than  when  the  hands  are  at  the  side.  "When  a 
book  is  used  in  reading,  it  should  be  generall}'  held  in  the  left 
hand  so  that  the  right  is  free  to  turn  the  leaf. 

The  errors  in  the  position  of  the  hands  are  those  of  place 
and  form.     The   errors  of  the  first  class  are, — putting   the 


TEACHING    READING    OR   ELOCUTION.  207 

hands  in  the  pockets,  placing  them  on  the  hips,  playing  with 
a  button  or  the  watch-guard,  or  Avith  any  portion  of  the  dress, 
frequent  changes  as  if  tiie  person  did  not  know  what  to  do 
with  the  hands,  etc.  The  errors  of  the  second  class  are, — 
spreading  the  fingers,  closing  the  fingers  too  tightly,  sticking 
out  the  thumb,  straightening  out  the  hand,  closing  the  hand 
into  a  fist,  etc.  The  teacher  should  carefullj^  note  and  correct 
all  errors,  and  secure  a  natural,  easy,  and  graceful  position  of 
the  hands. 

Tlie  Head. — The  head  gives  the  chief  grace  to  the  person, 
and  is  an  important  element  in  deliverj-.  The  position  of  the 
head  should  be  erect  and  natural.  It  should  not  droop,  which 
indicates  humility  or  diffidence ;  nor  be  thrown  back,  which 
indicates  arrogance  and  pride  ;  nor  be  inclined  to  one  side, 
which  indicates  languor,  indifference,  or  clownishness  ;  nor 
be  held  too  stiff,  which  indicates  a  lack  of  ease  and  self-pos- 
session. 

The  Body. — The  position  of  the  body  should  be  erect,  easy, 
and  natural,  with  the  breast  fully  fronting  the  audience.  The 
shoulders  should  be  thrown  gently  back,  so  as  to  give  the  full- 
est freedom  and  capacity  to  the  organs  of  the  chest.  The 
errors  to  be  avoided  are,  leaning  forward  or  backward,  round- 
ing the  shoulders,  leaning  to  one  side,  and  being  too  rigidly 
erect. 

How  Teach. — In  teaching  posture,  the  teacher  should  him- 
self be  able  to  present  a  model  for  imitation.  He  should  be 
careful  to  correct  all  errors  of  feet,  body,  head,  arms,  hands,  etc. 
He  should  also  make  his  pupils  familiar  with  the  principles  of 
posture.  There  is  a  natural  language  of  posture,  a  language 
common  to  all  times  and  races.  For  these  principles,  see  works 
on  Elocution. 

TTT  Gesture. — By  Gesture  is  meant  the  movement  of  the 
body  and  its  members.  It  is  a  visible  manifestation  of  thought 
and  sentiment  which  accompanies  its  oral  expression.  Gesture 
is  one  of  the  most  important  concomitants  of  elocution.     Some 


208  METHODS   OF  TEACHING. 

writer  remarks,  "In  the  natural  order  of  passionate  expres- 
sion, looks  are  first,  gestures  second,  and  words  last."  De- 
mosthenes, when  asked  what  are  the  requisites  of  an  orator, 
replied,  "  Action,  action,  action." 

Gesture  is  the  natural  lano-uage  of  thouijht  and  sentiment. 
It  is  a  universal  language,  understood  by  all  people.  No  matter 
what  their  speech,  all  know  the  meaning  of  gestui'es,  and  can 
communicate  with  one  another  thereby.  An  entire  play  can 
be  presented  in  pantomime  so  as  to  be  fully  understood.  Ges- 
ture is  visible  language,  apparent  to  the  eye  as  the  spoken 
sound  is  to  the  ear.  When  combined  with  speech,  it  is  thus 
easy  to  see  how  it  enforces  the  sentiment  expressed.  Indeed, 
it  was  a  matter  of  dispute  between  Roscius  and  Cicero  which 
could  produce  the  greater  effect,  the  former  b3^  gesture,  or  the 
latter  by  spoken  words. 

Gestures  may  be  divided  into  three  classes  ;  those  of  Loca- 
tion^ Illustration,  and  Emphasis.  Gestures  of  Location  are 
designed  to  indicate  the  position  of  the  object  or  idea  referred 
to.  Gestures  of  Illustration  are  designed  to  show  the  way 
in  which  something  appeared  or  was  affected.  Gestures  of 
Emphasis  are  designed  to  give  greater  intensity  to  the  mean- 
ing of  words  or  sentences  by  physical  movements. 

Eleuienfs  of  Gesture. — Gesture,  in  its  fullest  sense,  in- 
cludes the  Bow,  and  the  position  and  movement  of  the  Head, 
the  E^-es,  the  Arms,  the  Hands,  the  Body,  and  the  Legs  and 
Feet. 

The  Bow. — The  Bow  of  a  speaker  should  be  graceful,  easy, 
and  dignified.  It  should  be  free  from  a  careless,  jerking 
abruptness,  and  from  a  formal,  unnecessary  flourish.  It 
should  not  be  too  low,  so  as  to  seem  overdone,  nor  too  short, 
so  as  to  seem  trifling  or  disrespectful.  It  should  not  be  a 
mere  nod  of  the  head,  but  the  entire  body  should  be  slightly 
included  in  the  movement.  The  bod}-  should  be  bent  directly 
forward,  and  not  on  one  side.  The  foot  ma}'  be  slightly'  drawn 
back,  or  not,  as  is  preferred.     Some  teachers  prefer  that  there 


TEACHING    READING    OR   ELOCUTION.  209 

shall  be  a  step  backward  subsequent  to  the  bow ;  but  this  is  a 
matter  of  taste,  and  is  not  essential. 

The  Hands. — The  Hands  are  the  most  important  members 
In  gesture.  As  Quintilian  remarks,  these  almost  speak  them- 
selves. "  By  them  we  ask,  promise,  call,  dismiss,  threaten, 
supplicate,  detest,  fear;  display  jo}*,  sorrow,  doubt,  acknowl- 
edgment, penitence,  manner,  abundance,  number,  time."  "So 
that  amid  the  great  diversity  of  language  among  all  races  and 
nations,  this  appears  to  me  to  be  the  common  speech  of  all 
men." 

The  Form  of  the  hand  in  making  gesture  should  be  natural 
and  unconstrained.  The  fino;ers  should  lie  near  one  another, 
slightly  curved,  the  thumb  being  pai'allel  with  the  fingers. 
The  gesture  with  the  forefinger  is  sometimes  appropriate,  and 
is  very  expressive  when  the  finger  is  long  and  slender.  A 
gesture  with  the  fist  is  very  seldom  allowable.  The  errors  of 
gesture  are,  fingers  straight  and  rigid,  too  much  apart,  too 
closely  pressed  together,  thumb  projected  from  the  hand,  etc. 

The  Position  of  the  hand  in  an  ordinary  gesture  of  empha- 
sis, should  be  a  little  above  the  waist,  between  the  waist  and 
shoulder.  In  referring  to  anything  above  one,  or  to  grand 
and  lofty  sentiments,  it  should  be  elevated  ;  in  referring  to 
anything  situated  low,  or  to  any  low,  debased  sentiment,  etc., 
it  should  be  below  the  ordinary  position. 

The  Movements  of  the  hand  should  be  srraceful  and  in  ffood 
taste.  The  hand  should  be  raised  in  curved,  and  not  in 
straight  lines;  and  the  movements  should  also  be  in  gently 
curving  lines.  Gestures  will  thus  embod3'  the  elements  of 
grace  and  beautj*.  Care  should  be  taken  that  the  movements 
and  transitions  be  not  abrupt  or  angular.  After  a  gesture, 
the  hand  should  fall  gently  and  naturally  to  its  place,  and  not 
go  down  with  a  jerk,  or  with  an  awkward  restraint. 

The  Arm. — The  Arm,  when  not  used  in  g-esture,  should  hanar 
naturally  at  the  side.  In  gesture,  the  elbow  should  be  slightly 
bent,  except  in  the  most  emphatic  gestures,  when  it  may  ofteii 


210  METHODS   OF   TEACHING. 

be  rigid  and  straight.     Care  should  be  taken  not  to  exhibit  an 
angle  at  the  elbow. 

The  Eyes. — The  Eyes,  -which  are  an  important  element  of 
expression,  should  generally  be  directed  as  the  gesture  points, 
except  when  we  wish  to  condemn,  refuse,  or  require  any  object 
to  be  removed.  The  eye  should  rest  upon  the  audience,  not 
with  a  familiar  stare,  but  with  a  kindly,  modest,  and  dignified 
expression.  To  show  a  modest  confidence  in  your  audience 
goes  very  far  to  secure  their  confidence  and  sympathy. 

How  Teach. — The  teacher  should  be  able  to  present  a  model 
in  gesture  worthy  of  the  imitation  of  the  pupil.  He  should  also 
make  the  pupil  familiar  with  the  general  principles  which  express 
the  natural  relation  between  the  sentiment  and  the  gesture.  He 
should  also  be  careful  to  correct  all  awkwardness  of  manner,  in- 
appropriateness  of  movement,  etc. 

Principle. — The  first  principle  of  gesture  is  that  it  should  be 
natural  and  appropriate.  The  second  principle  is  that  it  should  be 
graceful,  moving  in  fluent  and  connected  lines,  and  not  abrupt  and 
desultory.  A  third  principle  is  that  strong,  bold,  determined,  and 
abrupt  expressions  require  straight  lines;  while  all  beautiful,  grace- 
ful, grave,  grand,  and  exultant  sentiments  require  curved  lines. 

We  determine  the  force  and  extent  of  the  gesture  by  the  senti- 
ment expressed.  If  the  sentiment  is  unemotional,  as  in  ordinary 
conversation,  the  gestures  are  moderate,  the  movement  being 
mainly  from  the  elbow.  If  the  sentiment  is  earnest,  lofty,  and 
sublime,  as  in  oratory,  the  gesture  is  strong  and  wide,  the  arm 
moving  mainly  from  the  shoulder.  If  the  sentiment  is  highly 
impassioned,  as  in  dramatic  composition,  the  gestures  are  still 
more  vigorous  and  extended. 

Correct  Errors. — Do  not  allow  too  many  gestures.  Excess 
of  gesture  is  like  redundancy  of  language,  in  bad  taste  and 
tiresome.  Too  few  gestures  are  better  than  too  many.  Inex- 
pressive or  meaningless  gestures  should  be  avoided.  No  ges- 
ture should  be  made  without  a  reason  for  it.  Some  speakers 
accompany   nearly   every  word   with   a    bodily   motion,    which 


TEACHING    REAInXG    OR    ELOCLTTIOX,  211 

fatigues  the  eye  and  offends  the  taste.  A  gesture  that  illus- 
trates nothing  is  worse  than  useless  ;  it  destro^-s  the  effect  at 
which  it  aims.  When  a  gesture  has  been  assumed,  there 
should  be  no  change  from  it  without  a  reason.  Tne  habit  of 
allowing  the  hands  to  fall  to  the  side  immediately-  after  a 
gesture,  produces  an  ungraceful  and  restless  effect. 

IV.  Facial  Expression. — The  face  is  the  mirror  of  the 
mind.  By  nature  it  reflects  promptly  all  changes  of  senti- 
ment and  feeling.  It  is  therefore  one  of  the  most  important 
elements  of  expression.  A  voice  may  be  artistic  in  its  mod- 
ulations, it  ma3-  attune  itself  harmoniously  to  language,  l)ut 
if  the  soul  of  the  speaker  docs  not  shine  out  from  the  coun- 
tenance, much  of  the  power  of  expression  is  lost. 

All  the  great  speakers  and  writers  on  oratory  have  under- 
stood the  power  of  facial  expression.  Quintilian  sa3"s,  "  The 
face  is  the  dominant  power  of  expression.  With  this  we  sup- 
plicate; with  this  we  soothe;  with  this  we  mourn;  with  this 
we  rejoice;  with  this  we  triumph;  with  this  we  make  our  sub- 
missions ;  upon  this  the  audience  hang ;  upon  this  the}'  keep 
their  e^'es  fixed ;  this  the}'  examine  and  study  even  before  a 
word  is  spoken." 

Elements  of  Facial  Expression. — The  principal  features 
in  facial  expression  are  the  eyes  and  the  mouth,  though  the 
brow  and  cheeks  aid  in  exj)ression. 

The  Eyes. — The  eye  is  the  window  of  the  soul.  Out  of  it 
the  soul  seems  to  shine,  and  the  heart  can  be  read  by  peeping 
in  the  eyes.  "  When  there  is  love  in  the  heart,"  says  Beecher, 
"  there  are  rainbows  in  the  eyes."  "  The  eye,"  says  Tucker- 
man,  "  speaks  with  an  eloquence  and  truthfulness  surpass- 
ing speech.  It  is  the  window  out  of  which  the  winged 
thoughts  fl}'  unwittingly.  It  is  the  tin}'  magic  mirror  on 
whose  crystal  surface  the  moods  of  feeling  fitfully  play,  like 
the  simlight  and  shadows  on  a  still  stream."  Many  writers 
speak  of  "the  mute  eloquence  of  a  look ;"  and  Byron  sings  of 
eyes  which  "looked  love  to  eyes  that  spake  again." 


212  METHODS    OF    TEACHING. 

Tlie  Mouth. — The  mouth  is  even  more  expressive  than  the 
eyes.  The  peculiar  character  of  the  face  is  largely  due  to  the 
size  and  shape  of  the  mouth.  A  small  mouth  indicates 
secretiveness ;  a  large  mouth,  open-heartedness  and  good 
humor ;  parted  lips  iudicate  listlessness  or  stupidity ;  com- 
pressed lips  are  a  sign  of  firmness  and  decision  of  character ;  etc. 

The  expression  of  the  mouth  is  due  principally  to  the 
corners  of  the  mouth.  We  draw  up  the  corners  of  the  mouth 
in  laughing,  and  depress  them  in  crying.  "To  be  down  in 
the  mouth"  is  an  expi-essive  phrase  for  low  spirits.  In  a 
picture  the  same  face  may  be  changed  from  laughter  to  weep- 
ing by  merely  making  a  change  in  the  corners  of  the  mouth. 

How  Teach. — In  facial  expression  nature  must  be  our 
guide.  The  soul  must  feel  the  sentiment  to  be  expressed,  and 
the  countenance  must  be  the  mirror  of  the  soul.  The  play  of 
features  must  respond  to  the  sentiment  stirring  in  the  heart. 
The  following  propositions  will  indicate  the  general  principles 
of  facial  expression. 

Unemotional  sentiments  require  the  countenance  to  be  in 
repose.  Sentiments  of  good  humor,  happiness,  etc.,  require  a 
pleasant  and  smiling  countenance.  Bold,  grand,  and  noble 
sentiments  require  dignity  and  animation  of  countenance. 
Humorous  sentiments  require  the  play  of  humor  in  the  face ; 
sad  and  pathetic  sentiment  should  be  accompanied  with  a 
dejected  and  softened  expression ;  shame  requires  the  averted 
eyes  and  blush  of  guilt.  Determination,  anger,  and  a  spirit 
of  defiance  are  expressed  by  a  contracted  brow  and  com- 
pressed lips  ;  in  scorn  we  elevate  the  upper  lip  and  nose  ;  in 
fear,  surprise,  and  secresy,  the  brow  is  raised,  the  eyes  are 
opened,  and  the  lips  parted. 

General  Suggestions. — We  close  this  chapter  on  Reading 
with  two  or  three  philosophical  and  practical  suggestions. 

Reading  is  an  Art,  and  the  basis  of  all  Art  is  Nature.  The 
object  of  culture  in  Elocution  is  therefore  natural  expression.  It 
aims  not  to  eliminate,  but  to  train  and  improve  the  natural 


TEACHING    READING  OR   ELOCUTION.  213 

expression.  Everything  artificial  in  expression  is  regarded  as 
inartistic  and  distasteful.  The  reader  who  "shows  his  elocution" 
in  his  reading,  offends  good  taste,  and  shows  his  shallowness  of 
mind  and  the  imperfection  of  his  art.  In  elocution  especially, 
we  should  endeavor  to  attain  that  excellent  standard  of  culture 
in  which  "the  highest  art  conceals  art." 

We  are  to  look  for  natural  expression  in  conversation.  Con- 
versation is  the  simplest  and  most  common  form  of  human  ex- 
pression. "  It  contains  the  germs  of  all  speech  and  action,"  and 
thus  constitutes  the  basis  of  all  correct  delivery.  The  importance 
of  cultivating  correct  habits  of  voice  and  manner  in  conversation 
cannot  be  over-estimated.  Conversation  is  a  beautiful  art,  and 
deserves  culture  for  its  own  sake,  and  also  as  a  basis  of  elocu- 
tionary culture. 

The  standard  by  which  we  judge  of  good  reading  is  a  cultivated 
taste.  Man  possesses  an  sesthetic  nature,  which  when  properly 
cultivated  by  the  influence  of  natural  expression  in  art,  enables 
him  to  sit  in  criticism  upon  the  productions  of  the  artist.  Where, 
through  personal  idiosyncrasies,  tastes  seem  to  differ,  we  are  to  be 
controlled  in  our  decision  by  the  opinions  of  the  majority  of  cul- 
tivated persons. 

In  conclusion,  we  urge  teachers  to  remember  that  elocution  is 
a  beautiful  art,  and  worthy  of  the  highest  culture.  Voice  and 
speech  are  divine  gifts,  and  should  be  trained  to  their  highest 
excellence.  As  Prof.  Shoemaker  so  well  remarks,  "  It  is  only  the 
voice  that  has  reached  its  best,  and  the  eye  that  beams  from  the 
soul,  and  the  hand  of  grace,  and  the  attitude  of  manhood  and 
womanhood,  that  can  convey  the  immortality  that  has  been 
breathed  upon  us."  As  God  manifests  His  glorious  attributes  in 
the  expression  of  Nature  and  the  Bible,  and  above  all  in  the 
Eternal  Word,  so  may  we  show  the  image  of  divinity  in  our  souls 
by  a  pure,  natural,  beautiful,  and  artistic  expression. 


CHAPTER   VII. 

TEACHING   LEXICOLOGY. 

LEXICOLOGY  treats  of  the  meaning  of  words.  The  terra 
is  derived  from  lexicon,  a  dictionary,  and  logos,  a  dis- 
course. It  is  usually  emplo^'ed  to  embrace  the  origin  and 
significance  of  words  ;  but  it  is  here  used  as  relating  only  to 
the  meaning  and  proper  use  of  words. 

The  meaning  of  words  is  largely  taught  in  all  the  branches 
of  language.  The  subject,  consequently,  does  not  need  a 
lengthy  treatment  b}'  itself.  No  formal  study  of  the  subject 
is  suggested  for  the  ordinarj'^  common  school;  but  much  can 
be  done  in  all  the  studies  to  lead  pu2^ils  to  notice  new  words, 
learn  their  meaning,  and  fix  them  in  their  memory.  In  the 
higher  classes,  oral  lessons  might  be  given  on  the  subject;  and 
in  advanced  schools  there  should  be  a  regular  course  of  study 
to  teach  the  meaning  and  use  of  words.  A  few  suggestions 
will  be  made  to  guide  the  teacher  in  his  work. 

B]f  their  Use — The  meaning  of  words  is  taught  by  their 
use  in  conversation  and  speaking.  The  child  first  learns  the 
meaning  of  words  from  the  mother  and  father  and  other  mem- 
bers  of  the  household.  The  words  he  uses  have  never  been 
explained  to  him;  no  definitions  have  been  given  him ;  but  he 
uses  them  correctly  because  he  has  heard  them  so  used.  Usage 
is  his  guide  in  using  language.  If  he  has  been  accustomed  to 
hearing  a  correct  and  refined  vocabulary,  he  will  express 
himself  with  correctness  and  refinement.  It  is  of  inestimable 
advantage  in  linguistic  culture  to  listen  to  the  conversation 
ot  intelligent  and  cultivated  people.  It  is  said  that  the 
Gracchi  obtained  the  elegant  use  of  language  from  their 
accomplished  mother  Cornelia ;  and  Aristotle  imbibed  from 

(214) 


TEACHING    LEXICOLOGY.  215 

his  mother  "  that  pure  and  sweet  Atticism  which  ever^wliere 
pervades  his  writings," 

By  lleuduxj. — The  meaning  of  words  is  learned  from  read- 
ing. This  is  one  of  the  most  practical  ways  in  which  such  a 
knoAvledge  is  acquired.  In  literature  we  see  the  correct  use 
of  the  word,  which  we  cannot  alwa^'s  tell  from  the  definition. 
We  also  learn  to  appreciate  those  nice  shades  of  meaning 
which  cannot  be  stated  in  a  definition.  Pupils  who  read  most 
have  usually  the  largest  vocabularj'  and  the  best  use  of  words. 
Young  children  will  often  be  heard  using  the  words  in  their 
conversation  which  they  have  met  with  in  some  book  recently 
read;  and,  if  properly  taught,  their  compositions  will  show 
the  same  thing.  Children  sliould  therefore  be  encouraged  to 
read  extensively  and  to  read  the  best  written  Avorks. 

Teachers  should  call  attention  to  the  meaning  and  use  of 
words  in  the  reading  lesson.  Tiiey  should  require  pupils  to 
put  the  unusual  and  difficult  words  into  sentences  to  see  that 
they  know  how  to  use  them.  In  tliis  way  the  word  is  fixed 
in  the  memory-,  and  the  child's  vocabulary  enlarged.  The 
reading  class  presents  one  of  the  very  best  opportunities  for 
teaching  the  meaning  of  words. 

By  Illustrations. — With  3'oung  pupils,  the  meaning  of 
words  may  be  taught  hy  means  of  objects  or  illustrations. 
Thus,  the  meaning  of  the  word  transparent  may  be  illustrated 
with  a  piece  of  clear  glass ;  the  meaning  of  the  word  translu- 
cent, by  a  piece  of  ground  or  painted  glass  ;  the  word  opaque. 
by  any  object  which  does  not  permit  the  light  to  pass  through 
it.  The  best  way  to  teach  the  meaning  of  the  word  bone  is  to  show 
the  pupils  a  bone ;  and  the  same  may  be  said  of  calyx,  corolla, 
stamen,  pistil,  etc.  Most  of  the  terms  of  the  natural  sciences 
may  be  taught  in  this  way,  and  many  of  those  in  the  abstract 
sciences,  as  the  names  of  the  figures  in  geometry.  Object 
Lessons  are  especially  vahiable  in  this  respect. 

By  Definitions. — The  meaning  of  words  may  be  taught  l)v 
incans  of  popular  definitions.     The  unknown  word   may  be 


216  METHODS   OF   TEACHIN^Q. 

made  known  hy  comparing  it  with  oa^  already  understood,  or 
b}'  the  use  of  several  words  which  explain  it.  Care  should  be 
iaken,  however,  that  the  term  used  in  the  definition  is  simpler 
or  better  known  than  the  word  defined.  This  is  not  always  the 
case  with  the  definitions  given  in  our  text-books,  especially 
tliose  found  in  some  of  our  school  readers.  To  define  shorten 
as  abbreviate,  or  correct  as  rectify,  or  buying  as  purchasing,  or 
belong  as  appertain,  etc.,  gives  the  pupil  another  word  for  the 
same  idea,  but  does  not  give  him  any  new  idea  of  the  first 
word. 

The  Dictionary. — The  ineaning  of  words  can  be  taught  by 
a  careful  use  of  the  dictionary.  Pupils,  as  soon  as  they  are 
old  enough,  should  be  required  to  make  frequent  use  of  the 
dictionary.  This  should  become  a  habit  with  them.  The 
great  masters  of  language  made  the  dictionary  their  constant 
compani(jn.  Rufus  Choate,  so  eminent  for  his  scholarly  use 
of  the  English  language,  was  a  constant  and  thorough  student 
of  the  dictionary. 

In  the  stud}-  of  definitions,  it  should  be  remembered  that 
we  cannot  always  know  how  to  use  a  word  from  its  definition. 
Thus  abandon  means  to  forsake,  to  give  up,  etc.;  but  it  would 
not  be  correct  to  say  we  "forsake  a  study"  or  even  "abandon 
a  bad  habit,"  etc.  Abbreviate  means  to  shorten,  but  we  would 
not  appropriately  speak  of  abbreviating  a  dress  or  a  string  or 
a  stick  of  timber.  We  must  notice  the  use  of  words  in  sen- 
tences in  order  to  understand  the  nice  distinctions  between 
them;  and  definitions  should  alwa^'s  be  accompanied  by  sen- 
tences illustrating  the  proper  use  of  the  term  defined. 

A  pupil  should  acquire  the  habit  of  marking  down  every 
new  word  which  he  meets,  or  every  word  which  he  thinks  is 
not  a  part  of  his  practical  vocabulary.  He  should  keep  a  list 
of  such  words,  frequently  refer  to  them,  and  make  use  of  them 
in  speaking  and  writing.  He  will  thus  enlarge  his  stock  of 
words,  and  learn  to  use  them  with  readiness  and  precision  of 
meaninof. 


TEACHING    LEXICOLOGY.  217 

From  St/nonf/tna. — The  meaning  of  words  may  be  taught 
by  the  study  of  synonyms.  By  synonyms  we  mean  words  of 
the  same  general  significance,  3-et  with  slight  shades  of  ditter- 
ence  in  their  meaning.  They  are  words  which,  with  great  and 
essential  resemblances  of  meaning,  have,  at  the  sauie  time, 
small,  subordinate,  and  partial  ditferences.  These  ditferences 
may  have  originally  inhered  in  them,  or  thev  mav  have  ac- 
quirad  them  by  general  usage,  or  some  earh'  and  latent  mean- 
ing ma}'  have  been  awakened  by  the  special  usage  of  some 
"  wise   and   discreet  master  of  the  tongue." 

The  English  language  is  especiall}^  rich  in  sj'non3'ms.  This 
arises  from  its  being  a  composite  language,  words  for  the  same 
thing  being  derived  from  ditlerent  sources.  Many  of  these 
in  time  became  differentiated  and  now  constitute  our  syno- 
nyms. Thus  motherly  and  maternal,  fatherly  and  paternal, 
happiness  a,nd  felicity,  daily  and  diurnal,  poicerful  and  poten- 
tial, etc.,  are  pairs  of  words  meaning  very  nearly  the  same, 
the  first  in  each  case  coming  from  the  Anglo-Saxon  and  the 
second  from  the  Latin. 

The  study  of  synonjms  is  especially'  valuable  in  learning  to 
use  words  correctly.  It  enables  the  pupil  to  see  those  nicer 
and  more  delicate  shades  of  meaning  by  which  words  are  dis- 
tinguished. It  enables  them  to  see  in  what  cases  words  may 
be  used  interchangeably,  and  where  they  cannot  be;  thus  we 
may  say  force  of  mind  or  strength  of  mind,  but  not  strength 
of  gravitation.  It  is  onl}'  by  a  careful  comparison  of  words 
that  a  pupil  can  use  such  words  as  the  following  correctly: 
invent  said  discover  ;  only  and  alone ;  enough  and  sufficient , 
avow,  acknowledge,  and  confess;  kill,  murder,  and  assassinate 
Crabb's  Dictionary  of  Synonyms  is  an  excellent  work  for 
such  a  study,  though  the  subject  is  quite  full}'  presented  in 
Webster's  and  Worcester's  large  dictionaries. 

Loffical  Definitions. — The  meaning  of  words  maybe  taught 
by  means  of  logical  definitions.     A   logical  definition   is  one 
which   defines  by  means  of  the  class  and  specific  ditlerence, 
10 


218  METHODS   OF   TEACHING. 

called  genus  and  differentia.  Thus,  a  triangle  is  a  polygon  of 
three  sides  and  three  angles.  Here  polygon  is  the  genus^  and 
Uiree-nidedness  the  sjtecijic  difference.  The  practice  of  study- 
ing logical  definitions  tends  to  sharpen  our  conceptions  of 
the  distinction  of  words,  and  to  cultivate  the  habit  of  careful 
discrimination  in  the  use  of  language. 

Many  terms  will  not  admit  of  a  logical  definition.  Such  a 
definition  is  only  possible  when  the  genus  and  specific  differ- 
once  can  both  be  stated.  Terms  expressing  simple  ideas  can- 
not be  logieall}'  delined,  because  they  cannot  be  i-esolved  into 
their  elements,  and  are  thus  without  gen  as  and  differentia. 
Thus,  truth,  space^  being,  etc.,  will  not  admit  of  a  logical  defi- 
nition. Some  terms,  though  belonging  to  a  genus,  cannot  be 
defined  on  ace. unit  of  our  being  unable  to  state  the  differentia. 
Thus,  in  the  statement  red  is  a  color,  color  is  the  genus,  but 
who  can  give  the  differentia,  the  difference  that  separates  red 
from  the  other  colors? 

Latin  and  Greek. — The  meaning  of  words  may  be  learned 
by  the  Htudy  of  Latin  and  Greek.  The  practice  of  looking  in 
the  dictionary  to  find  the  English  words  which  correspond  to 
the  words  in  other  languages,  makes  the  pupil  familiar  with 
the  meanina:  and  use  of  the  English  words.  The  constant  use 
and  comi)arison  of  words,  iiecessar3'  in  translation,  give 
linguistic  accuracy  and  a  facility  in  their  use.  The  process 
of  translating  cultivates  that  fine  literary  sense  by  which  the 
delicate  shades  of  meaning  among  words  are  perceived  and 
appreciated. 

From  Etijmoloffij — The  meaning  of  words  may  be  taught 
by  the  study  of  Etymology.  A  knowledge  of  the  origin  of  a 
word  sometimes  aids  us  in  understanding  its  meaning  and  use. 
Thus  it  adds  to  our  idea  of  the  word  Education  to  know  that 
it  means  to  draw  out,  e  and  duco,  and  also  subtraction,  to 
know  that  it  means  to  draw  from  under,  sub  and  traho.  The 
etymology  often  enriches  and  enlarges  the  meaning  of  a 
word,  and  puts  an  exjn-essiveuess  in  it  by  the  image  it  brings 
before  the  mind  as  we  use  it. 


TEACHING   LEXICOLOGY.  219 

We  cannot  alwaj's  use  a  word  correctly,  however,  by  know- 
ing its  etymology.  Indeed,  the  etymology  of  a  word  would 
usually  lead  us  astray  in  its  use.  Thus  the  word  subtraction, 
even,  could  not  be  used  in  its  literal  etymological  sense  of 
dr  awing  from  under.  The  same  may  be  said  of  right,  wrong, 
conduct,  normal,  and  a  multiplicity  of  words  which  could  be 
named.  The  principal  use  of  et^^mology,  aside  from  the  inter- 
est and  intrinsic  value  of  the  knowledge,  is  that  it  puts  into 
the  mind  a  concrete  image  which  seems  to  add  force  oi  em- 
phasis to  the  meaning  of  a  term. 

There  are  two  methods  of  teaching  etymology;  the  Ana- 
lytic Method  and  the  Synthetic  Alethod.  The  Analytic  Method 
begins  with  the  word  as  a  whole  and  separates  it  into  its  ety- 
mological parts,  showing  the  meaning  of  the  parts,  and  thus 
the  meaning  of  their  synthesis  in  the  word.  Thus,  after  the 
child  is  familiar  with  the  word  subtraction,  it  may  be  shown 
that  it  consists  of  the  three  jDarts,  sub  meaning  under,  tract 
from  traho,  I  draw,  and  ion,  the  act  of.  A  large  number  of 
words  may  be  analyzed  in  this  way  as  they  occur,  and  a 
knowledge  of  the  elements  be  reached  through  the  words. 

The  Synthetic  Method  begins  by  teaching  a  list  of  prefixes 
and  suffixes  and  roots,  and  then  unites  them  in  forming 
words.  Thus,  after  committing  elements,  the  pupil  may  be 
shown  that  sub  and  tract,  a  modification  of  traho,  and  ion, 
give  the  word  subtraction.  In  actual  practice,  there  is  a  sort 
of  analysis  of  each  word  into  the  elements  which  have  been 
previously'  learned  ;  but  the  spirit  of  the  process  is  synthetic, 
since  it  passes  from  the  elements  to  the  word  containing 
them. 

Of  these  two  methods,  the  analytic  is  the  better  for  begin- 
ners. It  is  the  more  interesting  method  ;  the  committing 
of  a  list  of  roots  is  rather  dry  work.  It  is  also  in  accordance 
with  the  law  of  instruction,  from  the  known  to  the  unknoivn; 
while  the  synthetic  method  inverts  this  law.  It  also  begins 
in  the  concrete,  while  the  other  is  abstract.     For  advanced 


220  METHODS   OF   TEACHIXQ. 

pupils  the  synthetic  method  may  be  preferred,  as  it  is  more 
formal  and  thorough  in  its  procedure. 

Teachers  should  take  pains  to  call  the  attention  of  pupils 
to  the  etj-mology  of  words.  Even  some  incidental  instruction 
of  this  kind  will  give  the  pupil  a  knowledge  of  the  elements 
of  a  large  number  of  words;  and,  what  is  better,  cultivate  a 
taste  for  et3'molog3-.  They  should  not  restrict  their  instruc- 
tion to  Latin  and  Greek  elements,  but  should  call  attention 
to  the  Saxon  elements  also.  Such  words  as  England^  '^'^f^-, 
husband,  knave,  heathen,  etc.,  will  be  full  of  interest  to  chil- 
dren. Every  teacher  should  have  a  coj)}'  of  "Trench  on  the 
Study  of  Words,"  and  besides  this  it  would  be  well  for  them 
to  read  Max  Miiller,  Whitney,  Scheie  de  Vere,  etc. 


CHAPTER  VIII. 

TEACHING   ENGLISH   GRAMMAR. 

GRAMMAR  is  the  science  of  sentences.  English  Grammar 
is  the  science  of  the  English  sentence.  It  treats  of  the 
relation  and  construction  of  words  in  sentences.  In  other 
words,  grammar  is  the  science  of  the  sentential  use  of  words. 
The  term  grammar  seems  to  have  been  derived  from  gramma^ 
a  letter,  which  came  from  grapho,  I  write. 

Grammar  has  sometimes  been  defined  as  "  the  science  of 
language."  This  definition  includes  too  much,  for  there 
are  several  other  branches  of  lansruage  coordinate  with  gram- 
mar,  as  Rhetoric,  Etymology,  Philology,  etc.  It  is  sometimes 
defined  as  "the  science  which  teaches  us  to  speak  and  write 
the  English  language  correctly ;"  but  this  also  includes  too 
much,  as  other  branches  aim  at  the  same  result.  A  sentence 
may  be  grammatically  correct  and  still  be  incorrect  in  regard 
to  other  departments  of  language.  Besides,  it  is  not  proper 
to  define  a  science  as  "  that  which  teaches"  something. 

There  is  so  close  a  relation  between  grammar  and  the  two 
branches,  Rhetoi-ic  and  Logic,  that  it  is  difficult  to  state 
clearly  the  distinction  between  them.  Logic  is  the  science  of 
thought;  but  since  this  thought  must  be  expressed,  Logic 
deals  also  to  some  extent  with  the  expression  of  thought. 
Rhetoric  also  treats  of  the  manner  in  which  thought  and  senti- 
ment are  expressed.  Popularly  we  may  say, — Logic  teaches 
clearness  of  expression ;  Grammar,  correctness  of  expression  ; 
and  Rhetoric,  elfectiveness  of  expression.  Fowler,  in  attempt 
ing  to  distinguish  these  three  branches,  says :  "  Logic  deals 
with  the  meaning  of  language;  Grammar  with  its  construction ; 
and  Rhetoric  with  its  persuasiveness.     Logic  plans  the  tern- 

(221) 


222  METHODS   OF  TEACHING. 

pie;  Grammar  builds  it;  Rhetoric  adorns  it."  It  is  clear  thai 
since  thought  determines  expression,  the  science  of  logic  is 
very  intimately  related  to  a  full  understanding  of  the  subject 
of  Grammar. 

The  term  Grammar  was  formerly  used  in  a  broader  sense 
than  at  the  present  day.  In  its  widest  acceptation,  and  this 
was  its  primary  use,  it  included  all  verbal  expression  of  the 
products  of  the  mind.  Trench  says,  "Grammar  is  the  logic 
of  speech,  even  as  Logic  is  the  grammar  of  reason."  It  has 
also  been  used  to  signify  a  treatise  on  the  elements  or  princi- 
ples of  an}'  science;  as,  a  "grammar  of  geography,"  a  "gram- 
mar of  arithmetic."  The  terra  has,  however,  become  differ- 
entiated so  as  to  be  now  restricted  to  the  sentential  use  of 
words. 

I.  General  Nature  of  the  Subject. 

I.  Nature  op  Grammar. — To  aid  the  student  in  understand- 
ing the  methods  o/  teaching  grammar,  we  shall  present  a  brief 
statement  of  the  nature  of  the  science.  A  conception  of  the 
subject  of  grammar  may  be  presented  in  two  ways  ;  first,  b^'' 
considering  the  office  of  the  individual  words  in  a  sentence ; 
and  second,  b}^  resolving  the  sentence  into  the  thought 
elements  which  enter  into  its  structure.  The  former  is  called 
the  Etymological  view  of  grammar  ;  the  latter  is  called  the 
Logical  view  of  the  subject. 

Etynioloffical  Elements. — Language  is  made  up  of  indi- 
vidual words.  These  words  are  all  embraced  under  a  few 
general  classes,  some  eight  or  ten,  called  Parts  of  Speech. 
Each  one  of  these  parts  of  speech  performs  a  certain  office  in 
a  sentence,  and  some  perform  two  or  three  offices. 

Parts  of  Speech. — The  first  and  simplest  class  of  words  are 
those  which  are  the  names  of  objects,  called  Nouns.  There 
are  also  words  expressing  some  action  or  state  of  the  objects 
named  by  these  nouns,  which  are  called  Verbs.  Then  there  is 
a  cJass  of  words,  usually  expressing  qualities,  which  are  added 


TEACHING   ENGLISH   GRAMMAR  223 

to  the  nouns  to  distinguish  the  objects  referred  to  b^'  the 
noun  ;  these  are  called  Adjectives.  Tlien  we  have  a  class  of 
words  used  to  distinguish  the  actions  expressed  by  the  verbs, 
called  Adverbs.  The  words  used  to  distinguish  the  qualities 
exin-essed  by  adjectives  and  by  adverbs  are  also  called  adverbs. 

Then  there  is  a  class  of  words  used  for  nouns,  called  Pro- 
nouns. There  is  also  a  class  of  words  used  to  connect  other 
words  and  show  the  relation  between  them,  called  Preposi- 
tions. We  have  also  words  which  connect  words  and  sen- 
tences without  showing  any  relation  between  the  words 
connected,  which  are  called  Conjunctions.  There  are  words 
also  which  express  feelings  or  emotions,  which  on  account  of 
their  being  thrown  into  the  sentences  formed  by  other  words, 
are  called  Interjections. 

Properties  of  Parts  cf  Speech. — These  parts  of  speech  have 
certain  relations  to  one  another  and  to  the  things  which  they 
express,  that  give  rise  to  certain  changes  in  their  form  or 
meaning.  These  changes  in  form  are  called  Inflections,  from 
flecto,  I  bend,  since  the  form  of  the  word  is  changed,  as  in 
bending  an  object  we  change  its  form.  Words  which  admit 
of  such  changes  are  said  to  be  declinable^  from  c?e,  down,  and 
clino,  I  lean  or  incline.  In  many  cases  in  the  English  lan- 
guage there  is  no  change  of  form  to  indicate  the  relation, 
though  the  relation  really  exists,  and  is  thought  if  it  cannot 
be  seen.  These  are  all  embraced  under  the  head  of  the  Prop- 
erties of  the  parts  of  speech. 

The  pi'operties  of  the  Noun  are  Number,  Person,  Gender^ 
and  Case.  The  properties  of  the  Verb  are  Mode,  Tense,  and 
Voice,  and  also  Person  and  Number  derived  from  its  subject. 
The  change  in  the  adjective  and  adverb  is  called  Compar-ison. 
In  some  languages  the  adjective  has  the  properties  of  number 
and  case,  which  it  seems  to  have  derived  from  the  noun. 

CVfls-ses  of  Parts  of  Speech. — These  Parts  of  Sj^eech  admit 
of  various  divisions  into  classes,  which  give  us  what  are  called 
the  Classes  of  the  Parts  of  Speech.     Thus,  Nouns  are  divided 


224  METHODS   OF   TEACHING. 

into  Proper  and  Common,  etc.;  Verbs  into  Regular  and  Irreg- 
ular^ Transitive  and  Intransitive,  Qlc;  Pronouns  into  Per- 
sonal, Relative,  Interrogative,  eta. \  Conjunctions  into  Coor- 
dinate and  Subordinate ;  etc. 

Rules  of  Construction. — From  the  consideration  of  tlie  rela- 
tion of  these  words  to  one  another,  and  a  careful  examination 
of  the  usage  of  cultivated  men  and  women,  we  derive  certain 
laws  of  construction,  which  constitute  the  Rules  of  Grammar. 

Some  Offices. — Then  we  have  certain  offices  ascribed  to  the 
words  as  limit,  modify,  govern,  etc.  One  word  is  said  to 
limit  another  when  it  limits  its  application  to  a  part  of  the 
class  of  objects  which  it  represents ;  thus,  in  the  expression 
blue  birds,  the  word  blue  limits  the  word  birds  to  only  a  part 
of  the  general  class  of  birds.  The  term  modify  means  very 
nearly  the  same  as  limit,  one  word  modifying  the  application 
of  another  word  ;  as  in  red  roses,  the  i-ed  modifies  the  applica- 
tion of  the  word  roses.  By  government  in  grammar  is  meant 
the  power  that  one  word  is  supposed  to  exercise  over  another 
word  to  cause  it  to  assume  some  particular  form  or  meaning. 

Logical  Elements. — In  this  statement  we  have  a  brief  out- 
line of  the  nature  of  grammar,  derived  from  the  consideration  of 
the  individual  words  in  a  sentence.  There  is  another  method 
of  conceiving  the  subject,  however,  which  consists  in  deter- 
mining the  elements  of  language  by  regarding  the  sentence  as 
a  unit,  and  analyzing  it  into  the  necessary  parts  of  which  it 
is  composed.     We  state  briefly  the  results  of  such  an  analysis. 

Principal  Elements. — A  sentence  is  an  assertion  of  some- 
thing about  something.  Every  sentence  thus  contains  two 
necessary  elements ;  that  about  which  an  assertion  is  made, 
and  that  which  is  asserted.  These  two  elements  are  distin- 
guished as  the  Subject  and  the  Predicate.  The  Subject  may 
consist  of  a  single  word,  or  of  a  collection  of  Avords  not  form- 
ing a  proposition,  called  a  phrase,  or  of  a  collection  of  words 
containing  a  proposition,  called  a  clause.  Similarly,  the  Pred- 
icate may  consist  of  a  word,  a,  phrase,  or  a  clause. 


TEACHING    ENGLISH    GRAMMAR.  225 

Subordinate  Elements. — Continuing  the  analysis,  we  find 
that  some  elements  are  used  to  limit,  modify,  or  describe 
other  elements,  and  these  we  call  modifying  or  limiting  ele- 
ments. When  they  limit  the  meaning  or  application  of  words 
used  as  the  names  of  objects,  they  are  called  adjective  ele- 
ments; when  they  limit  the  meaning  or  application  of  words 
used  to  express  actions  or  qualities,  they  are  called  adverbial 
elements.  These  elements  are  often  called  adjuncts,  because 
they  are  joined  to  the  elements  which  they  limit.  To  distin- 
guish them  from  the  subject  and  predicate,  they  are  called 
subordinate  elements,  the  subject  and  predicate  being  called 
principal  elements.  These  subordinate  elements  are,  with 
respect  to  their  form,  of  three  classes ;  words,  phrases,  and 
clauses;  and  with  respect  to  their  use  thej^  are  also  of  three 
classes;  adjective,  adverbial,  and  objective. 

Connective  Elements. — In  addition  to  the  principal  and  sub- 
ordinate elements,  there  are  also  words  used  to  connect  the 
other  elements,  which  are  called  connective  elements.  We 
also  often  find  in  language  words  that  have  no  logical  connec- 
tion with  the  other  words;  such  words  are  called  independent 
elements.  This  method  of  looking  at  a  sentence  and  reaching;  its 
elements  may  be  called  the  logical  method,  in  distinction  from 
the  other  methcd.  which  niay  be  called  the  etymological  method. 

II.  Origin  of  Grammatical  Elements. — Having  pointed  out 
the  grammatical  elements  of  language,  the  questions  naturally 
arise, — How  did  these  elements  originate?  Why  have  we  just 
so  many  parts  of  speech  ;  and  wh}'  are  they  such  as  they  are? 
We  shall  endeavor  to  give  a  brief  reply  to  these  questions. 
There  are  two  theories  upon  this  subject;  one  drawn  from  the 
consideration  of  the  operation  of  the  several  faculties  of  the 
mind,  and  the  other  that  presented  by  the  writers  on  logic. 
These  two  views,  for  want  of  better  names,  we  may  distinguish 
as  a  New  and  the  Old  theory. 

A  New  Theory. — Language  is  the  product  of  the  human 
10* 


226  METHODS   OF   TEACHING. 

mind  The  thought  went  out  into  expression,  and  thus  gave 
form  to  the  language.  In  order,  therefore,  to  understand  the 
growth  and  nature  of  the  grammar  of  the  language,  we  must 
look  at  it  through  the  laws  of  mental  activity. 

Parts  of  Speech. — The  faculty  of  the  mind  which  first 
awakens  into  activity  is  Perception.  Perception  cognizes 
individual  things,  and  forms  particular  ideas.  These  ideas 
we  express  in  particular  words;  hence  our  first  words  are 
names  which  we  call  nouns,  from  nomen,  a  name.  These  names 
are  of  individuals  and  are  thus  proper  nouns,  or  have  the 
force  of  proper  nouns.  The  mind  also  sees  these  objects  act- 
ing or  doing  something,  which  it  expresses  in  the  form  of 
action  or  doing  xoords.  These  words  are  called  verbs,  from 
verbum,  a  word,  because  they  are  regarded  as  the  most  import- 
ant words  in  a  sentence.  These  verbs,  like  the  nouns,  at  first 
express  particular  actions. 

The  mind,  at  first,  cognizes  objects  as  wholes,  without  dis- 
tinctly noticing  their  attributes  ;  but  it  soon  begins  to  analyze 
them  and  to  distinguish  their  qualities  ;  the  naming  of  these 
qualities  in  their  relation  to  the  objects,  gives  us  words  to 
distinguish  objects,  which  on  account  of  their  being  added  to 
nouns,  we  may  call  adnouns;  or,  since  they  are  thrown  to 
nouns,  they  have  been  called  adjectives,  from  ad,  to,  a.ndjacio, 
I  throw.  The  mind  also  compares  actions  and  notices  their 
differences  ;  the  naming  of  these  differences  in  relation  to  the 
action,  gives  us  a  class  of  words  to  distinguish  actions;  which, 
on  account  of  their  being  added  to  verbs,  are  appropriately 
called  adverbs. 

The  mind  in  comparing  objects,  notices  these  similarities, 
and  brings  the  similar  objects  together  under  a  common  name; 
it  thus  forms  general  ideas  which  give  rise  to  general  terms  or 
common  nouns.  In  a  similar  manner,  the  verb,  which  was  at 
first  the  name  of  some  particular  action,  becomes  general  in  its 
application  to  a  class  of  similar  actions.  The  adjective  and  the 
adverb  also  become  more  general  as  our  experience  enlarges. 


TEACIIIXG    ENGLISH    GRAMMAR.  227 

llavins:  obtained  general  notions,  the  mind  begins  to  com- 
l)are  these  general  notions,  and  perceiving  a  relation  between 
them,  forms  judgments,  which  when  expressed,  give  ns  the 
proposition.  These  judgments  or  propositions  need  a  connect- 
ing or  athrming  word,  which  gives  rise  to  the  copula  or  neuter 
verb  as  "  nr.an  is  an  animal."  The  affirmation  of  an  attribute 
of  a  general  notion  (regarding  the  intension  of  the  concept) 
also  requires  the  use  of  the  copula,  as  "  man  is  mortal." 

As  our  progress  in  thought  and  language  continues,  it  is 
found  convenient  to  avoid  the  too  frequent  repetition  of  nouns, 
which  we  do  by  the  introduction  of  a  class  of  words  to  be 
usedybr  nouns,  which  we  call  for-nouns,  or  pronouns.  If  it 
were  riecessar}'  to  have  a  class  of  words  to  avoid  the  too  fre- 
quent repetition  of  the  verb,  we  should  have  a  class  of  for- 
verbs  or  pro-verbs  also,  which  we  seem  to  approximate  in  the 
peculiar  use  of  the  word  do;  as  "John  studies,  and  so  do  I." 

In  order  to  unite  and  show  the  relation  of  some  of  the 
words  we  use  in  the  construction  of  sentences,  it  was  neces- 
sary to  introduce  words  expressing  relations,  which  we  may 
call  relation-words ;  or,  since  the}'^  are  placed  before  the  word 
to  be  related  to  some  other  word,  they  are  called  prepositions, 
from  prae,  before,  and  pono,  I  place.  Words  used  merely  to 
conjoin  words  and  sentences  were  also  necessary,  and  were 
called  conjoining  words,  or  conjunctions.  Words  expressing 
emotions  were  also  needed,  and  since  these  words  had  no 
relation  to  the  rest  of  the  sentence,  but  were  thrown  in 
abruptly  between  other  words,  they  were  called  interjections, 
from  inter,  between,  and  Jacio,  I  throw. 

The  Properties. — We  may  also  account  for  the  origin  of  the 
inflections  or  properties  of  the  parts  of  speech  in  a  similar 
manner.  It  was  necessary  to  distinguish  between  the  use  of  a 
noun  as  meaning  one  or  more  than  one  object,  and  this  was  con- 
veniently done  by  a  change  of  termination  in  the  nouns  to  in- 
dicate this  meaning,  which  gave  rise  to  the  property  of  number 
For  all  practical  purposes  two  forms   were  sufficient ;  hence 


228  METHODS    OF    TEACHING. 

we  have  only  two  numbers,  singular  and  pIitraL  Some 
nations,  however,  seemed  to  find  it  convenient  to  distinguish 
between  one,  two,  and  more  than  two  things  ;  and  thus  arose 
a  third  form,  called  the  dual  number.  This  dual  form  is  sup- 
posed to  have  been  caused  by  the  duality  of  the  parts  of  the 
human  body,  as  the  eyes,  the  hands,  etc. 

Since  there  were  two  objects  of  the  same  class  of  animals 
distinguished  by  sex,  it  is  natural  that  words  should  be 
changed  in  their  form  to  distinguish  the  sex  of  the  object 
named  ;  and  thus  arose  the  property  of  gender.  Since  a  noun 
could  represent  the  three  persons,  the  speaker,  the  person 
spoken  to,  and  the  person  spoken  of,  there  naturally  arose  a 
change  of  form  in  the  noun  to  indicate  the  person  ;  which  gave 
rise  to  the  property,  called  the  person  of  nouns.  The  dirt'er- 
ent  relations  that  an  olyect  may  sustain  to  an  action  or  to 
another  object,  caused  a  change  of  termination  to  indicate  the 
relation  meant ;  and  this  gave  the  property  of  case,  six  in 
Latin  and  eight  in  Sanskrit.  In  our  language  these  relations- 
are  principally  exi)ressed  by  prepositions,  leaving  us  only 
three  cases  for  pronouns,  and,  some  say,  only  two  cases  for 
nouns,  the  nominative  and  the  possessive.  All  these  proper- 
ties of  nouns  would,  of  course,  belong  to  pronouns  as  their 
representatives. 

The  properties  of  the  verb  originated  in  a  similar  manner 
The  fact  that  a  verb  could  be  used  in  commanding,  or  inquir- 
ing, or  simply  declaring  an  action,  gave  rise  to  the  property 
of  the  manner  or  mode  of  the  verb.  The  idea  of  time  and  the 
fact  that  the  action  expressed  by  a  verb  could  take  place  in 
ditferent  times,  gave  rise  to  a  change  of  the  verb  to  indicate 
these  times  of  an  action,  which  produced  the  property  of  tense. 
It  was  natural  for  the  form  of  the  verb  to  vary  as  the  nutibei 
and  person  of  its  subject  varied  and  this  gave  rise  to  the 
number  and  person  of  the  verb. 

The  number  and  person  of  a  verb  are  not  intrinsic,  but  deriv- 
ative properties  of  the  verb ;  ^nd  by  some  grammarians  arc 


TEACUING    ENGLISH    GRAMMAR.  229 

not  regarded  as  properties  at  all.  A  certain  writer  saj's  that 
to  attribute  person  and  number  to  a  verb  is  "as  anomalous  as 
to  assign  gender  and  number  to  adjectives.  Most  languages 
fall  into  this  error,  which  is,  however,  susceptible  of  a  ver^' 
easy  historical  solution.  It  arose,  doubtless,  from  the  original 
custom  of  annexing  the  pronoun  to  the  termination  of  the 
verb,  and  continuing  the  use  of  the  inflection  after  its  import 
had  been  forgotten,  and  when  the  pronoun  had  been  formed 
into  an  independent  part  of  speech." 

It  seems  to  have  been  natural,  primaril^^,  to  express  the 
relation  of  words  by  an  affix  or  prefix  to  the  radical  portion 
of  the  word ;  these  changes  seem  subsequently  to  have  been 
replaced  by  particles.  The  earlier  stage  of  a  language  is  usu- 
ally richer  in  teriBinations  ;  which  drop  off  as  the  faculty  of 
abstraction  becomes  habitual.  In  a  manner  similar  to  that 
now  explained,  we  can  account  for  every  grammatical  distinc- 
tion by  a  development  from  the  natural  psychological  opera- 
tions which  give  form  to  language.  The  different  Classes  of 
parts  of  speech  arise  from  the  different  offices  performed  by 
words  of  the  same  general  class,  and  the  Rules  of  Construc- 
tion grew  out  of  the  laws  impressed  upon  language  by  thought, 
modified  by  the  circumstances  of  fashion,  etc.,  which  inti'o- 
duced  changes  into  the  language  of  the  people. 

The  Old  Theory. — We  have  thus  indicated  what  we  con- 
ceive to  be  a  correct  idea  of  the  development  of  grammatical 
elements  from  the  natural  operation  of  the  human  mind. 
There  is,  however,  another  view  of  the  subject,  drawn  from 
logic  rather  than  from  psychology.  We  will  briefly  indicate 
this  view. 

It  is  held  that  the  first  class  of  words  are  subslantives,  so 
called  because  they  are  conceived  as  standing  under  (sub- 
stans)  certain  qualities.  These  qualities  may  also  be  consid- 
ered as  substantives,  as  whiteness,  greenness ;  but  when  con- 
sidered in  relation  to  the  substances  of  which  they  are  proper- 
ties, the}'  constitute  a  second  class  of  words,  adjectives  or 


230  METHODS   OF    TEACHING. 

noun-adjectives.  A.  vonceptiou,  or  general  notion,  when 
formed,  is  capable  of  being  resolved  back  into  its  constituent 
parts  or  qualities;  and  the  attribution  of  a  quality'  to  a  sub- 
stance leads  to  a,  judgment ;  as  "Snow  is  white,"  the  sign  of 
the  attribution  being  called  the  copula.  When  the  quality 
is  combined  with  the  copula,  a  third  class  of  words  is  pro- 
duced, wiiich  we  call  verbs.  Thus,  instead  of  saying,  "the 
sun  is  bright,"  we  may  say  "  the  sun  shines."  A  verb  is 
thus  regarded  as  a  compound  part  of  speech,  consisting  of 
an  adjective  and  a  copula  or  affirmation.  These  three  parts 
of  speech — the  substantive,  the  adjective,  and  the  verb,  are 
called  the  primary  or  essential  parts  of  speech. 

The  adverb,  it  is  said,  derives  its  existence  from  the  difficulty 
of  defining  by  one  word  the  precise  qualit}'  of  a  particular 
object.  Words  are  needed  to  indicate  the  degree  of  the  quality 
expressed.  The  primarj-  use  of  the  adverb,  it  is  thus  seen,  is 
to  modif}'^  the  quality  or  attribute  expressed  b}'^  the  adjective 
and  the  verb.  Prepositions  are  said  to  express  relations  be- 
tween substances,  objective  relations;  while  conjunctions  may 
be  regarded  as  expressing  subjective  relations,  or  those  exist- 
ing between  judgments,  whether  of  mere  succession,  of  infer- 
ence, or  the  lilce.  The  other  grammatical  elements  would  be 
derived  ver^-  nearly  in  the  manner  previousl3'^  explained, 

III.  Origin  of  Grammar. — Grammar  originated  among  the 
Greeks.  It  seems  to  have  had  its  origin  about  the  second 
century  B.  C,  among  the  scholars  of  Alexandria.  Many  o^ 
them  were  engaged  in  preparing  correct  texts  of  the  Greek 
classics,  especially  of  Homer.  The  manuscripts  differed,  and 
the  correct  form  was  determined  by  a  comparison  with  the 
language  of  Homer.  They  were  thus  forced  to  pa}''  attention 
io  gi'ammatical  structure,  and  to  observe  the  laws  of  con- 
struction. The  first  real  Greek  grammar  was  that  of  Diony- 
sius  Thrax,  a  pupil  of  Aristarchus.  He  went  to  Rome  as  a 
teacher  about  the  time  of  Pompej',  and  wrote  a  practical 
grammar,  it  is  supposed,  for  the  use  of  his  pupils.    This  work 


TEACHING    EXGLISII    GKAMMAR.  231' 

was  the  foundation  of  grammar.  Later  writers  have  improved 
and  completed  it,  but  have  added  nothing  really  new  and 
original  in  principle. 

The  earliest  scientific  investigations  of  language  among  the 
Greeks  were  not  strictly  grammatical,  but  discussed  the  rela- 
tion of  thought  to  expression.  The  distinction  of  subject  and 
predicate,  and  even  the  technical  terms  of  case,  number,  and 
gender,  were  first  used  to  express  the  nature  of  thought,  and 
not  the  forms  of  language.  The  early  Greeks  had  a  very  slight 
knowledge  of  grammar  proper.  Plato  knew  the  iiou7i  and 
verb,  as  two  component  parts  of  speech.  Aristotle  added  con- 
junctions and  articles,  and  observed  the  distinctions  of  num- 
ber and  case.  The  word  article  with  him,  however,  meant  a 
socket  in  which  the  members  of  the  sentence  moved,  and  in- 
cluded many  more  words  than  at  present.  Before  Zenodotus, 
250  B.  C,  all  pronouns  were  simply  classed  as  sockets  or  arti- 
cles of  speech.  He  was  the  first  to  introduce  a  distinction 
between  personal  pronouns  and  mere  articles  or  articulations 
of  speech.  Aristotle  had  no  technical  terms,  as  singular  or 
plural,  and  does  not  allude  to  the  dual.  Zenodotus  seems  to 
have  been  the  first  to  observe  the  use  of  the  dual  in  the 
Homeric  poems,  and  changed  many  plurals  into  duals. 

The  first  attempt  at  an  English  grammar  was  FauVs  Acci- 
dence, an  English  introduction  to  Lill3''s  Latin  grammar, 
written  by  Dr.  John  Colet  in  1510.  Lill^^'s  grammar  received 
the  sanction  of  ro3'al  authority  and  was  the  exclusive  stand- 
ard in  England  for  more  than  300  years.  The  first  book 
treating  exclusively  of  English  grammar  was  written  by  Wil- 
liam Bullokar  in  1586.  During  the  next  century,  several  works 
on  grammar  were  written,  among  which  are  mentioned  one  by 
Ben  Jonson  (1634),  one  b}^  Dr.  John  Wallis  (1653)  in  Latin, 
and  one  by  William  Walker  (1684),  the  preceptor  of  Sir  Isaac; 
Newton, also  in  Latin.  In  1158,  Bishop  Lowth  pul)lislied  his 
celebrated  grammar,  an  excellent  work  from  which  Lindley 
Murray'  drcM"  most  of  his  materials.    Lindley  Murray  published 


2o2  METHODS    OF    TEACHING. 

his  first  grammar  in  1195,  and  his  Abridgement  in  1797,  a 
work  which  has  been  extensively  used  in  this  countr}'  and  in 
England.  The  annual  sale  of  the  book  in  England  has  been 
estimated  at  50,000  copies.  This  popular  work  was  largely 
derived  from  Lowth  and  Priestley,  and  owed  its  popularity 
to  its  practical  adaptation  to  the  work  of  the  school-room. 
The  number  of  grammars  published  in  this  country  is  legion; 
the  ablest  and  most  celebrated  is  that  of  Goold  Brown.  The 
first  to  develop  and  give  prominence  to  "grammatical  analy- 
sis," was  Prof.  S.  S.  Greene,  of  Brown  University. 

IV.  The  TEACHiNa  of  Grammar. — Having  spoken  of  the 
nature  of  grammar,  the  origin  of  the  grammatical  elements, 
and  the  historical  development  of  the  subject,  we  shall  now 
call  attention  to  the  manner  in  which  it  has  been  taught,  and 
the  different  methods  of  teaching  it. 

Gratnniar  Poorly  Taught. — Grammar  has  been  more 
poorly  taught  than  an}-  other  branch  in  the  public  schools. 
It  has  been  made  too  abstract  and  theoretical.  It  has  been 
taught  as  a  matter  of  memory,  and  not  of  judgment  and 
understanding.  It  has  been  a  committing  and  repeating  of 
definitions,  and  not  a  study  of  the  relation  of  words  in  sen- 
tences. It  has  been  a  study  of  text-books  on  grammar  instead 
of  a  study  of  the  subject  of  grammar.  It  has  been  a  memor- 
izing of  abstract  definitions  and  rules,  instead  of  a  practical 
application  of  them  to  the  improvement  of  a  pupil's  language. 
It  has  been  a  worrj'  and  a  waste  of  time  and  patience  ;  and  a 
labor  barren  of  adequate  results.  We  believe  we  are  correct 
in  saying  that  more  than  three-fourths  of  the  time  spent  in  the 
stud}'^  of  grammar  in  the  public  schools,  has  been  worse  than 
wasted. 

The  result  of  such  teaching  is  that  the  pupils  of  our  com- 
mon schools  go  out  with  a  much  better  knowledge  of  arithme- 
tic, geography,  etc.,  than  of  grammar.  Besides  this,  the 
methods  of  teaching  have  given  pupils  wrong  ideas  of  the  sub- 
ject and  incorrect  methods  of  studying  it.     Taught  b}'  reciuir- 


TEACHING   ENGLISH    GRAMMAR.  233 

ing  pupils  to  commit  and  recite  definitions,  tliey  have  come 
to  look  at  the  grammar  of  lan2:uao;e  throiis-h  the  definitions 
rather  than  at  the  definitions  through  language.  Pupils  thus 
taught  not  ouly  obtain  confused  notions  of  grammar,  but 
often  acquire  a  dislike  and  even  a  disgust  for  the  subject. 

These  errors  in  teaching  grammar  arise  from  two  sources ; 
the  defects  of  our  text-books  and  the  incompetency  of 
teachers.  The  books  have  been  defective  on  account  of 
their  beginning  with  definitions  instead  of  exercises  to  lead 
to  definitions.  They  have  presented  the  matter  too  ab- 
stractly. They  have  not  aimed  to  lead  the  pui)il  to  apply 
his  knowledge  of  the  subject.  They  have  not  been  pro- 
perly graded ;  and  have  introduced  difficulties  before  the 
pupil  was  prepared  for  them.  They  have  been  constructed  on 
the  deductive  method  of  teaching,  instead  of  the  inductive 
method,  as  all  primar}'  grammars  should  be.  A  change, 
however,  is  taking  place  in  this  respect;  some  of  the  more 
recent  text-books  on  primary  grammar  being  a  great  improve- 
ment on  the  old  ones. 

The  incompetency  of  teachers,  stated  as  the  second  cause  of 
this  poor  teaching,  has  been  not  so  much  in  their  imperfect 
knowledge  of  grammar  as  in  their  defective  methods  of  teach- 
ing it.  Teachers  of  the  public  schools  usually  know  enough 
grammar  for  their  work,  but  they  do  not  know  how  to  teach 
it.  Having  been  incorrectly  instructed  themselves,  and  hav- 
ing received  no  instruction  in  the  true  method  of  teaching  it, 
the^^  reproduce  the  same  faulty  methods  in  their  own  work, 
and  thus  the  evil  is  perpetuated. 

The  difficulty  which  pupils  experience  in  learning  grammar 
is  entirely  unnecessary.  When  properly  taught,  grammar  is 
one  of  the  easier  studies  of  the  common  school  course.  In- 
trinsically, the  elements  of  grammar  are  less  difficult  than  the 
elements  of  arithmetic  :  a  knowledge  of  grammar,  such  as  is 
contained  in  an  ordinary  common  school  text-book,  is  much 
more  readily  acquired  than  the  same  amount  of  arithmetic 


234:  METHODS   OF   TEACHING. 

Grammar  can  also  be  made  one  of  the  most  interesting  studies 
of  the  public  school,  by  teaching  it  according  to  a  proper 
metliod.  I  have  never  seen  children  more  interested  in  any 
classes  than  in  the  primary  grammar  class  when  correctly 
taught. 

Methods  of  Teachinfj. — There  are  two  distinct  methods  of 
teaching  grammar;  the  Synthetic  or  ^Etymological  Method, 
and  the  Analytic  or  Logical  Method.  The  Syutlietic  or  ¥A\- 
mological  method  begins  with  the  word^^,  regarded  as  hdiUoJ 
language,  and  proceeds  to  sentences.  It  regards  the  words  as 
parts  of  speech,  denoting  objects,  actions,  qualifies,  etc.,  and 
not  as  logical  elements  of  thought.  It  is  called  Syutlietic  be- 
cause it  proceeds  from  words  to  their  combination  in  sen- 
tences. It  is  called  Etymological  because  it  deals  with  the 
parts  of  speech  as  words. 

The  Analytical  or  Logical  method  of  teaching  grammar 
begins  with  the  sentence  as  i\xQunit  of  language, and  analyzes 
it  into  its  thought  elements.  It  considers  the  sentence  as  con- 
sisting of  two  principal  elements,  the  subject  and  predicate, 
passes  from  these  to  subordinate  and  connective  elements,  and 
at  last  reaches  the  words  as  parts  of  speech.  It  first  regards 
words  not  as  parts  of  speech,  but  as  expressing  the  logical  ele- 
ments of  which  a  sentence  is  composed.  It  is  called  Analyt- 
ical, because  it  passes  from  the  sentence  as  a  whole  to  the  parts 
composing  it.  It  is  called  Logical,  because  it  deals  with  the 
logical  elements  out  of  which  sentences  are  composed. 

The  ditierence  between  these  two  methods  is  radical  and 
important.  Thus,  by  the  former  raetliod,  a  yioun  is  taught  as 
a,  name;  by  the  latter  method  it  is  regarded  as  expressing 
that  of  which  something  is  said.  By  the  former  method  a 
verb  expresses  an  action  or  doing ;  by  the  latter,  it  expresses 
ivhat  is  affirmed  or  asserted  of  the  subject.  An  adjective,  liy 
the  former  method,  is  the  name  of  a  quality  of  an  object;  by 
the  latter  method  it  is  regarded  as  a  word  which  limits  the 
extent  of  a  general  conception  or  the  application  of  a  general 


TEACHING   ENGLISH    GRAMMAR.  235 

term.  Thus,  by  the  logical  method,  good,  in  the  expression^ 
good  boys,  is  not  regarded  as  expressing  the  quality  or  kind 
of  boys,  but  as  limiting  the  concept  boys  to  a  portion  of  its 
extent,  or  the  term  boys  to  part  of  the  class.  So  the  adverb 
limits  the  general  action  to  some  particular  action :  thus,  in  the 
sentence.  The  bird  fies  swiftly,  the  flying,  which,  without  the 
adverb  swiftly,  would  include  all  kinds  of  flying,  is  here  limited 
to  a  particular  kind  of  flying ;  namely,  swift  flying.  By  the 
Etymological  method,  the  preposition  is  taught  as  expressing 
the  relation  of  objects ;  by  the  Logical  method  it  is  taught  as 
the  connecting  part  of  an  adjunct  or  subordinate  element. 

It  should  be  observed  that  the  two  methods  are  not  dis- 
tinguished merely  by  one  beginning  and  the  other  not  begin- 
ning with  a  sentence.  We  may  begin  with  a  sentence  and 
teach  by  the  etymological  method,  by  regarding  the  words  of 
the  sentence  as  parts  of  speech.  In  teaching  by  the  synthetic 
method  we  should  use  the  sentence  as  well  as  by  the  analytic 
method.  The  essential  diflerence  is  not  in  the  use  or  non-use 
of  the  sentence,  but  in  the  manner  of  using  it.  In  one  case  we 
begin  with  the  words  as  parts  of  speech  ;  in  the  other  case  we 
bcin  with  the  loijical  elements  of  a  sentence,  and  come  down 
to  the  words  as  parts  of  speech  through  these  logical  elements. 

The  Correct  MetJiod. — In  teaching  grammar,  neither  one 
of  these  methods  should  be  followed  exclusively,  but  they  should 
be  judiciously  combined.  Both  are  needed  to  give  a  complete 
knowledge  of  grammar,  and  each  will  aid  the  other  in  giving 
clearer  ideas  of  the  subject  than  can  be  obtained  by  either  one 
alone.  From  a  generalization  of  the  use  of  words  as  parts  of  speech 
the  pupil  is  naturally  and  easily  led  to  grammatical  analysis  ;  and 
from  some  of  the  distinctions  in  grammatical  analysis  much 
clearer  notions  of  the  correct  use  and  relation  of  words  as  parts 
of  speech  can  be  presented.  Both  methods  are,  therefore,  essen- 
tial to  a  complete  system  of  grammatical  instruction,  and  they 
should  go  hand  in  hand  in  unfolding  the  subject  in  the  mind  of 
the  learner. 


236  METHODS   OF   TEACHING. 

The  etymological  method  will  serve  as  a  valuable  introduction 
to  the  logical  method.  The  use  of  words  as  the  elements  of  sen- 
tences will  prepare  for  the  use  of  collections  of  words  as  express- 
ing these  elements.  Thus  from  the  use  of  single  words  as  parts  of 
speech,  the  pupil  is  easily  led  to  see  that  phrases  and  clauses  may 
perform  these  same  offices.  From  a  word  used  as  a  notui  or  an 
adjective  or  an  adverb,  etc.,  it  is  readily  seen  how  a  phrase  or  a 
clause  may  be  used  as  a  noun,  adjective,  or  adverb,  etc. 

The  logical  method  will  also  be  of  great  advantage  in  under- 
standing the  use  of  words  as  parts  of  speech.  Thus  the  concep- 
tion of  a  phrase  as  a  modifier  of  a  noun  or  a  verb  indicates  the 
antecedent  term  of  the  relation  of  a  preposition,  which  is  not 
ahvays  readily  seen  without  this  conception.  Much  clearer  ideas 
of  indirect  objects,  adverbial  objects,  relative  pronouns,  etc.,  will 
be  obtained  by  the  logical  analysis  of  sentences.  Indeed,  analysis 
will  aid  in  giving  clearer  ideas  of  nearly  every  part  of  the  subject 
than  can  be  obtained  by  the  etymological  method  alone. 

The  correct  order  of  these  two  methods,  it  would  seem,  is  to 
begin  with  the  etymological  and  pass  gradually  to  the  logical 
method.  Several  reasons  can  be  given  for  this  order.  First,  the 
etymological  method  is  simpler  in  thought  than  the  logical 
jaethod,  and  is  much  more  easily  understood  by  young  pupils. 
Second,  it  coincides  with  the  natural  method  by  which  they  learn 
language ;  first  words,  and  then  sentences.  A  little  child  begins 
language  with  words  as  the  names  of  objects  rather  than  with 
sentences  or  propositions.  Its  adjectives  are  at  first  the  names 
of  qualities  rather  than  limiting  elements  of  general  conceptions. 

This  order  is  also  to  be  preferred  because  it  ibllows  the  law, 
from  the  particular  to  the  general.  "Grammatical  Analysis"  is, 
to  a  large  extent,  a  generalization  of  the  principles  of  etymological 
grammar.  Thus,  at  first,  we  see  that  a  single  word  is  a  part  of 
speech,  as  an  adjective;  and  later  we  learn  that  a  phrase  or  a  clause 
may  be  used  as  an  adjective,  and  is  thus  an  adjective  element  of  a 
sentence.  The  same  is  true  in  respect  to  the  noun,  the  adverb, 
etc. ;  in  each  case  there  is  a  generalization  Irom  the  use  of  words, 


TEACHING  ENGLISH   GRAMMAR.  237 

to  tte  similar  use  of  phrases  and  clauses.  The  order  also  cor- 
responds with  the  historical  development  of  the  subject,  for  "gram- 
matical analysis"  is  of  comparatively  recent  origin  and  was  a 
development  of  etymological  grammar. 

The  proper  combination  of  these  methods,  it  seems  to  me,  is  as 
follows  :  First,  give  the  pupils  an  elementary  knowledge  of  words 
as  parts  of  speech.  Second,  give  the  pupils  a  general  notion  of 
the  logical  analysis  of  sentences.  Third,  then  present  a  detailed 
treatment  of  the  parts  of  speech  including  their  classes  and 
properties.  In  connection  with  this  third  division  have  constant 
exercises  in  parsing,  analysis,  and  the  correction  of  false  syntax. 
Such  a  combination  of  the  two  methods  will  produce  the  happiest 
results  in  teaching  English  grammar. 

Principles  of  Teaching  Grammar, — In  teaching  gram- 
mar by  either  of  these  two  methods,  the  teacher  should  be 
guided  in  his  work  by  the  following  principles  of  instruction: 

1.  Teach  first  by  means  of  oral  exercises.  Do  not  l)egin  bj' 
having  pupils  stud}'  definitions  from  a  text-book.  No  gram- 
mar-book is  needed  for  several  months,  with  a  class  l)Oginning 
grammar.  In  an  ordinary  common  school,  I  should  use  no 
text-book  on  the  subject  for  at  least  six  months  or  a  year.  A 
school  reader  may  be  used  for  examples  of  parts  of  speech, 
for  parsing,  etc.  A  text-book  in  grammar  is  a  positive  dis- 
advantage to  a  beginner.  It  seems  to  stand  as  a  partition 
wall  between  the  pupil's  mind  and  the  subject.  It  causes  him 
to  "  see  through  a  glass"  very  darkly  that  which  is  simple  and 
clear  without  the  book. 

2.  Teach  grammar  from  language  and  not  from  definitions. 
The  old  way  was  to  begin  with  definitions ;  the  correct  method 
is  to  begin  with  language.  In  this  way  the  pupil  will  see  and 
understand  the  grammatical  use  of  words,  while  by  the  old 
method  he  recited  their  use  without  understanding  it.  By 
the  former  method,  he  depends  on  what  the  book  says  ;  by  the 
latter  method,  he  learns  to  depend  on  his  own  judgment  in 
determining  the  nature  and  relation  of  words.  In  one  case, 
he  looks  at  grammar  through  the  definitions ;  in  the  other  case 


238  METHODS   OF   TEACHING. 

he  looks  at  grammar  through  the  nature  of  the  sulyect  itself 
In  the  former  case,  grammar  is  too  much  a  matter  of  memory ; 
in  the  latter  case,  it  is  a  matter  of  the  judgment  and  the  un- 
derstanding. Let  grammar,  therefore,  be  taught  from  lan- 
guage, as  it  was  originally  developed  by  those  who  first  inves- 
tigated it. 

An  additional  reason  for  teaching  primary'  grammar  from 
language  without  a  text-book,  is  that  the  proper  study  of  the 
subject  is  especiall}' an  act  of  the  judgment.  There  are  very 
few  things  to  commit  to  memory  in  elementar}*  grammar. 
There  are  a  few  technical  terms  which  are  readily  remembered 
when  the  pupil  has  the  ideas  which  they  express.  What  we 
especially  need  is  to  examine  language  and  notice  the  rela- 
tions of  words  ;  and  not  to  commit  and  recite  definitions. 
There  is  no  other  study  in  the  public  school  that  so  little  needs 
a  text-book  as  the  first  lessons  in  grammar ;  and  assuredly 
there  is  no  study  in  which  the  text-book  is  so  much  of  a  hind- 
rance to  the  beofinner  as  this.  Some  of  the  most  successful 
teachers  of  advanced  classes  in  grammar  use  an  edition  of 
some  of  the  favorite  poems  of  our  eminent  authors  as  the  text- 
book for  the  lesson,  while  the  real  text-book  is  used  only  as  a 
work  of  reference. 

3.  Make  the  sentence  the  basis  of  grammatical  instruction. 
Though  we  begin  with  words,  we  should  pass  as  soon  as  pos- 
sible to  sentences,  and  study  the  words  with  respect  to  their 
relations  in  sentences.  Grammar  treats  of  the  sentential  use 
of  words,  and  it  is  only  by  viewing  their  relations  in  sentences 
that  we  can  understand  their  grammatical  meaning  and  use. 
In  teaching  grammar,  therefore,  the  sentence  is  to  be  regarded 
as  the  unit  of  reference.  But  though  we  make  use  of  the  sen- 
tence in  instruction,  we  are  to  consider,  first,  not  the  logical 
use  of  the  words  in  it,  but  their  etj'mological  use.  The  words 
in  the  sentence  are  to  be  regarded  as  etymological  elements 
expressing  objects,  actions,  etc.,  and  not  the  logical  elements 
of  wliich  sentences  are  composed. 


TEACHING    ENGLISH    GRAMMAR.  239 

4.  Make  the  subject  practical.  We  should  require  the 
pupils  to  use  good  grammar ;  to  apply  what  they  learn  in 
moulding  and  correcting  their  own  speech.  We  should 
excite  an  interest  among  pupils  in  the  use  of  correct  lan- 
iTuaafe,  and  in  correcting  their  mistakes.  Have  them  bring 
in  false  sj-ntax  heard  in  the  school-room  and  on  the  play- 
ground. Let  the  teacher  be  careful  to  use  correct  language 
himself,  as  an  example  to  his  pupils. 

5.  The  course  in  grammar  should  be  preceded  by  a  course 
of  instruction  in  Language  Lessons.  The  basis  of  instruction 
in  grammar  is  language,  and  a  pupil  should  have  some  lessons 
in  language  before  he  begins  the  subject  of  technical  grammar. 
Such  a  course  of  lessons  is  indicated  under  the  methods  of 
teaching  Composition. 

Time  to  Uegin. — The  time  to  begin  grammar  depends 
upon  the  manner  in  which  it  is  taught.  If  presented  Induc- 
tivel}',  with  oral  exercises,  the  pupil  may  begin  the  study  at 
nine  or  ten  years  of  age.  The  average  age  for  the  pupils  of 
our  common  schools  is  probably  about  ten  or  twelve.  If, 
however,  grammar  is  taught  by  the  old  method  from  the  text- 
book, it  should  not  be  commenced  before  the  age  of  fifteen  or 
sixteen. 

Division  of  Subject. — For  the  purpose  of  instruction, 
grammar  may  be  divided  into  Primary  Grammar  and  Ad- 
vanced Grammar.  For  Primary'  Grammar,  the  sj'nthetic  or 
etymological  method  of  teaching  is  employed  as  the  basis  of 
instruction  ;  in  Advanced  Grammar  the  analytic  or  logical 
method  should  be  made  more  prominent.  We  shall  indicate 
a  course  of  instruction  in  both. 

II.  Method  of  Teaching  Primary  Grammar^ 

By  Primary  Grammar  is  meant  such  a  course  of  instruction 
in  grammar  as  shall  present  the  fundamental  facts  and  princi- 
ples of  the  science.  It  is  designed  to  lay  the  foundation  of 
grammatical   knowledge,    but   does   not   extend    to   the   higher 


240  METHODS   OF   TEACHING. 

philosophical  principles  of  the  science,  nor  discuss  the  anoma- 
lies of  construction,  etc. 

Principles  of  Instruction — There  are  several  principles 
of  instruction  that  should  be  made  especially  prominent  in  a 
primary  course  in  grammar.  They  are  principles  that  have 
been  previously  announced  ;  but  so  important  are  they,  and 
so  often  are  they  violated  in  grammatical  instruction,  that  we 
repeat  them  here. 

1.  Teach  first  the  idea  and  then  the  expression  of  it.  This 
principle  is  of  especial  importance  in  teaching  grammar.  The 
old  way  was  to  teach  the  expression  first,  and  often  the  pupil 
did  not  get  the  idea  at  all.  Both  teachers  and  pupils  have 
used  the  expressions,  "govern,"  "relates  to,"  "qualifies," 
"modifies,"  etc.,  for  years,  without  ever  thinking  what  they 
meant.  The  majority  of  teachers  of  whom  we  have  inquired, 
What  do  you  mean  by  "  prepositions  govern  the  objective 
case  ?  "  could  give  no  intelligent  explanation  of  its  meaning. 
Do  not,  therefore,  begin  witli  the  definition  as  the  statement 
of  the  idea,  but  present  the  idea  first,  and  then  lead  the 
pupils  to  the  expression  of  it. 

2.  Teach  pupils  to  discover  the  idea  you  wish  to  express. 
The  old  way  was  to  tell  the  pupil  everything  ;  the  better  way 
is  to  allow  him  to  discover  all  he  can  for  himself.  This  is  the 
inductive  method  of  instruction,  and  grammar  is  one  of  the 
very  best  studies  in  which  to  apply  the  inductive  method.  It 
will  make  the  pupil  a  thinker  in  grammar,  independent  of  the 
teacher  or  text-book. 

3.  Let  the  primary  aim  be  grammatical  ideas  rather  than 
grammatical  expressions.  Care  not  so  much  for  the  defini- 
tions as  for  the  idea  to  be  defined.  Do  not  require  definitions 
until  the  idea  is  clearly  developed  in  the  mind  of  the  learner, 
and  let  the  definition  flow  from  the  natural  expression  of  the 
idea. 

4.  Do  not  burden  the  memory  with  grammatical  forms.  A 
general  fault  in  teaching  grammar  is  that  the  subject  is  made 


TEACHING    ENGLISH   GRAMMAR.  241 

too  formal.  Too  much  attention  is  paid  to  the  manner  of 
expressing  grammatical  ideas.  In  Primary  Grammar,  the 
forms  of  parsing  and  anal\'sis  shoukl  be  very  simple.  We 
should  depend  more  upon  asking  pupils  questions  in  language 
than  upon  their  giving  any  set  forms  of  expression. 

The  Order  of  Instruction  in  this  subject,  in  accordance  with 
these  principles,  is  as  follows  :  1.  The  Idea ;  2.  The  Name ; 
3.  The  Definition  ;  4.  Exercises. 

The  Course  of  Instruction. — The  Course  of  Instruction  in 
Primary  Grammar  includes  the  following  things  :  1.  The 
Parts  of  Speech;  2.  The  Properties  and  Inflections;  3.  The 
Classes  of  the  Parts  of  Speech ;  4.  The  Rules  of  Construction  ; 
5.  The  Elements  of  Parsing;  6.  The  Elements  of  Analysis  ;  7. 
Correcting  False  Syntax. 

These  are  to  be  presented  somewhat  in  the  order  named, 
but  not  entirely  so.  We  should  begin  with  the  Parts  of 
Speech,  but  the  Classes  and  the  Inflections  may  be  taught 
somewhat  together ;  and  the  Elements  of  Parsing,  Analysis, 
and  the  Correcting  of  False  S^^ntax,  should  be  introduced 
gradually  as  the  pupils  are  prepared  for  them.  Tlie  above  is 
a  logical  division,  showing  what  is  to  be  taught  rather  than 
the  order  in  which  the  several  things  are  to  be  presented.  In 
presenting  the  subject,  we  shall  first  describe  the  method  of 
teaching,  and  then  follow  the  description  with  an  inductive 
lesson,  indicating  how  the  pupil  is  led  to  the  idea  and  its  ex 
pression,  by  appropriate  questions. 

I.  Parts  of  Speech. — We  begin  the  instruction  in  grammar, 
by  teaching  the  Parts  of  Speech.  In  order  to  prepare  for 
this,  we  should  give  to  the  pupil  a  clear  idea  of  an  object 
and  a  word.  This  can  be  done  by  showing  them  an  object, 
asking  its  name,  and  calling  attention  to  that  which  we  hear 
spoken,  or  see  written.     The  lesson  suggested  is  as  follows: 

Model  Lesson.— TeacJier,  holding  up  a  book,  a  knife,  etc.,  says,  What 
is  this?     Pupil.  K  book.     7'.  This?    P.  k  knife.     T.  What  do  we  call  all 
these  things  we  can  see,  touch,  etc.?    P.   Objects.     T.  What  do  we  call 
11 


242  METHODS    OF   TEACHING. 

those  things  we  hear  when  we  speak  ?  P.  Words.  T.  Are  there  any 
words  besides  those  we  liear  f  P.  Yes,  words  we  can  see.  P.  What 
shah  we  call  the  words  we  can  see  ?  P.  Seen  icords.  T.  Since  we  write 
these  words,  what  may  we  call  them  ?  P.  Written  words.  T.  What  may 
we  call  the  words  we  hear?  P.  Heard  words.  T.  Since  we  speak  them, 
what  kind  of  words  may  we  call  tliem?  P.  Spoken  words.  T.  How 
many  kinds  of  words  then  have  we?  P.  Two  kinds;  spoken  words  and 
uTritten  words. 

The  Noun. — To  teach  a  Noun,  present  several  objects  to  the 
pupil,  have  him  name  them,  write  these  names  on  the  board, 
and  lead  him  to  call  them  object-words;  then  to  define  an 
object-word,  and  then  give  him  the  term  not(7i  as  meaning  the 
same  as  object-ivord,  and  have  him  define  a  noun.  Then  give 
exercises,  requiring  him  to  select  nouns  from  a  book,  and  to 
give  examples  of  nouns.  Then  teach  that  the  names  of  per- 
sons, places,  etc.,  begin  with  a  cajiital  letter. 

Jfiidd  Lesson. —  Tearher.  What  is  this  I  hold  in   my  book. 

hand?     Pupil.  A  book.   T.  What  is  this?     P.  A  knife.  ^"^f''- 

T.  This?     P.  A  pencil      T.  I  will  write  these  names  on  f„V'S\  n 

the  boird;  what  are  these  in  my  hands?  P.  Objects. 
T.  What  are  these  on  the  l)()ard?  /-'.  Words.  T.  Wliat  are  these 
words  the  names  of?  P.  The  names  of  objects.  T.  Since  they  are  the 
names  of  objects,  what  kind  of  words  may  we  call  them?  P.  Object- 
words.  T.  What  then  h  im  object- word?  P.  An  object-word  is  tJie  name 
of  an  object. 

Tliey  have  thus  been  led  to  the  idea  of  an  object-word,  to 
name  it  themselves,  and  to  make  their  own  definition  of  it. 
The  next  step  is  to  require  them  to  name  and  write  object- 
words,  and  to  have  them  point  out  object-words  in  tlie  reader. 
After  they  are  familiar  with  object-words,  then  introduce  the 
name  noun.     The  exercise  is  as  follows  : 

Model  Lesson. — Teacher.  What  do  we  call  the  names  of  objects?  Pupil. 
Object-words.  T.  I  will  give  you  a  shorter  word  that  means  the  same  as 
object-word;  it  is  noun;  what  is  it  ?  P.  Noun.  T.  What  then  is  a  noun  ? 
P.  A  noun  is  an  nbjecf-irord.  T.  And  what  is  an  object-word  ?  P.  An 
object- word  is  the  name  of  an  object.  T.  Wliat  then  is  a  noun?  P.  A 
aoun  is  the  name  of  an  object. 

Ttie  Veih. — To  teach  the  Verb.,  we  call  the  pupil's  attention 


runs. 

plays. 

sings, 

eats. 

drinks. 

strikes. 


TEACHING   ENGLISH   GRAMMAR,  243 

to  the  actions  of  some  object,  write  a  list  of  words  expressing 
action  upon  the  board,  lead  the  pupils  to  call  them  action- 
icords,  and  define  an  action-word^  and  then,  after  they  are 
familiar  with  the  idea  and  name,  introduce  the  term  verb  as 
moaning  the  same  as  action-word,  and  lead  them  to  define  it, 
and  give  them  a  drill  on  the  verb  and  the  noun. 

Mod-el  Lesson. — Te<icJier.  Name  some  of  the  actions  of  a  child.     Pupil. 
A  child  runs,  plays,  sings,  eats,  drinks,  sleeps,  etc.  ' 

T.  Verj'  well,  I  will  write  these  on  the  board  in 
a  column  ;  what  are  these  words  the  names  of?  -P. 
The  names  of  actions.     T.  If  they  were  the  names  Cnila 

of  objects,  what  should  we  call  them  ?  P.  Object- 
words.  T.  Since  they  are  the  names  of  actions, 
what  may  we  call  them?    P.  Action-icords.     T. 

"What  then  is  an  (Z^ifOft-iconi'  P.  An  action- word  is  the  name  of  an 
action.  T.  Very  well  ;  there  is  a  little  word  that  means  the  same  as 
action-word  ;  it  is  vtrh  ;  what  is  it?  P.  Verb.  T.  What  then  is  a  verb  ? 
P.  A  verb  is  an  acfo"o«-zrorrf.  T.  And  what  is  an  action-icord?  P.  The 
name  of  an  action.  T.  How  then  may  we  define  a  verb?  P.  A  verb  is 
the  name  of  an  action  ;  or,  A  verb  is  a  word  that  expresses  action. 

Exercises.  -1.  Name  actions  of  difierent  objects.  2.  Name  objects  that 
can  do  different  actions.     3.  Select  nouns  and  verbs  in  the  reader. 

The  verb  may  also  be  taught  as  a  doing-word  instead  of  an 
actio7i-icord,  by  asking  what  a  child  can  do.  After  the  pupils 
are  familiar  with  the  primary  use  of  the  verb  as  expressing  an 
action,  they  should  be  led  to  see  that  the  verb  may  be  used  in 
making  a  statement,  asking  a  question,  or  giving  a  command ;  from 
which  an  accurate  definition  may  be  obtained. 

Tlie  Sentence. — We  should  next  unite  the  noun  and  verb  into 
sentences,  and  give  the  pupil  an  idea  of  the  sentence.  Then  teach 
the  three  kinds  of  sentences, — the  telling  or  declarative  sentence, 
the  asking  or  interrogative  sentence,  and  the  commanding  or  hnper- 
aiive  sentence.  Then  teach  them  to  write  sentences,  observing 
these  three  rules  :  1.  A  sentence  begins  with  a  capital  letter;  2.  A 
declarative  or  an  imperative  sentence  ends  with  a  period ;  3.  An 
interrogative  sentence  ends  with  an  interrogation  point.  The  sen- 
tence raav  also  be  presented  before  the  verb,  and  the  nature  of  the 
verb  taught  from  the  sentence. 


24:4:  METHODS    OF   TEACHING. 

Model  Lessoi. — Teaclier,  wrlLliig  the  -word  John  on  the  board,  asks  what 
he  has  written  on  the  board.  P'tpil.  The  word  John.  T.  Tell  me  some- 
thing Jolin  does.  P.  John  wnlka,  John  talks,  John  sings,  etc.  T.,  writing 
them  on  the  board,  says,  Such  expressions  as  these,  containing  a  noun 
and  a  verb,  in  which  the  verb  names  some  action  of  the  noun,  are 
called  sentences.  Make  some  sentences  about  ^lary,  a  bird,  a  horse,  etc. 
T.  What  might  a  sentence  which  tdh  something,  be  called  ?  P.  A  tell- 
ing senteiiee.  r.,  writing,  Ca7i  John  walk?  says,  Does  this  tell  anything 
ab'Ut  John?  P  No,  sir,  it  asks  a  question.  T.  Ver}' well, such  a  com- 
bination of  a  noun  and  a  verb  is  also  Ciilled  a  sentence.  Since  it  asks  a 
question,  what  kind  of  &  sentence  may  we  call  it?  P.  An  asking  sen- 
tence. T.,  writing,  John,  walk  fast,  may  by  similar  ([Uestions,  lead 
the  pupils  to  call  it  a  commanding  sentence. 

The  Adject  tie. — In  teacliing  iha  Adjeciice,  we  first  lead 
to  the  idea  of  quality.  We  do  tiiis  b}'  comparing  objects,  and 
having  pupils  name  the  ditferences,  and  telling  them  these  are 
called  the  qualUies'oT  the  objects,  ^e  then  get  a  list  of  the 
qualities  of  an  object,  and  then  lead  the  pupils  to  call  the 
words  qualit j-W07'dSy  or  quality-object-words,  and  define  the 
same  ;  we  then  introduce  the  term  adjective,  and  have  them 
define  it.  Before  giving  the  word  adjective  it  may  be  well  to 
lead  pupils  to  call  them  adnouns,  since  they  are  added  to 
nouns. 

Model  Lesson. — Teacher,  holding  op  two  objects,  as  a  pencil  and  card, 
"What  have  I  in  my  hands?    Pupils.  Pencil  and  card.     T.  Do  they  look 
alike?    P.  No,  sir.    7".  How  do  they  differ?    P.  One  is  ro//7;(f,  the  other 
I?,  flat ;  one  is  black,  the  other  is  tchite;  etc.     T.  Very  well;  these  things 
in  which  objects  differ  are  called  qualities  of  objects;  what  are  they 
Ciilled?    P.  Qualities  oT  objects.     T.  Name  some  qualities  of  an  apple. 
P.  Sicest,  sour, red,  yellow,  mellow,  ripe,  etc.     T.  We  will 
write  these  in  a  column  on  the  board ;  now  whiit  are  these        sweet. 
words  the  names  of?    P.  Qualities  of  objects.     T.  If  they        "'  ,  ' 
were  the  names  of  objects,  what  kind  of  words  should  we        yellow. 
call  them?      P    Object-words.      T.  Since  they  are  the        melloiD. 
names  of  qualities,  what  shall  we  call  them?    P.  Quality- 
words.     T.  Since  they  belong  to  objects,  what  kind  of  quality  words  may 
we  call  them?     P.  Qunlify-object-words.     Tl  What  then  is  si  quality -ob- 
jcct-uvrd?    P.  A  quality-object-word  is  the  name  of  a  quality  of  an  ob- 
ject.    T.  There  is  another  word  which  means  the  same  as  quality  object 


TEACHING   ENGLISH   GRAMMAR.  245 

word;  it  is  adjective;  wliat  is  it?  P.  Adjective.  T.  What,  then,  is  an 
adjective  ?  P.  An  adjective  is  a  qnality-ohject-word.  T.  And  wliat  is  a 
qunlity-object-icord?  P.  The  name  of  a  quality  of  an  object.  T.  What 
then  is  an  adjective  ?  P.  An  adjective  is  the  name  of  a  quality  of  an  object. 
Show  also  how  to  lead  the  pupil  to  call  them  adnouns. 

Exercises. — 1.  Name  the  tjualities  of  objects;  2.  Name  objects  having 
certain  qualities;  3.  Write  sentences  containing  givm  nouaa,  verbs,  and 
adjectives;  4.  Point  out  nouns,  verbs,  and  adjectives  in  the  reading  book. 

The  Adverb — We  taught  the  Adjective  by  comparing  ob- 
jects; we  should  teach  the  Adverb  b}^  comjyaring  aclioiis, 
since  the  adverb  bears  the  same  relation  to  actions  that  the 
adjective  does  to  objects.  We  begin  by  comparing  actions, 
obtain  a  number  of  words  which  distinguish  them,  write  these 
words  upon  the  board,  and  lead  the  pupil  to  call  them  qual- 
ity-action-ivords,  and  define  the  same;  and  then  introduce  the 
term  adverb  by  showing  that  the  quality -action-word  is  added 
to  a  verb,  and  lead  them  to  define  it. 

Model  Lesson. — Teacher,  moving  his  hand,  inquires,  What  am  I  doing? 
Pupil  Moving  j-our  hand.     2\  Look  and  see  if  these  motions  are  alike: 
how  does  it  move  now  ?     P.  Sloirly.     T.  How   does  it 
move  now?     P.  Fast,  or  quickly.     T.  How  does  it  move        slowly. 
now?     P.  Upward.      T.  How  does  it  move  now  ?     P.         5""<"'^ly- 
Downward,     Tl  Are  these  motions  alike  ?     7^.  No,  sir.         downward 
T.  What  words  distinguish  these  actions?     P  Slowly, 
quickly,  upward,  downward.     T.  What  did  we  call  those  things  in  which 
objects  differed?    P.  Qualities  of  objects.     T  What  shall  we  call  those 
things  in  which  actions  differ?     P.  Qualities  of  actions.      T.  What  shall 
we  call  those   words  tliat  name  the  qualities  of  actions?     P.  Quality- 
aetion-words.     T.  What  then  is  a.  quality-action-word  F  etc.,  etc.     To  lead 
to  the  term  adverb  write  "  hand  moves  slowly"  on  the  board.     T.  What 
is  slowly?     r.  To  what  word  is  slowly  a(7d<YZ,   hand  or  moves?    What 
part  of  speech  is  moves  ?    To  what  part  of  speech  then  is  slowly  added  ? 
If  it  is  added  to  a  verb,  what  may  we  call  it  ?    P.  Added  to  a  verb  f    T. 
Yes,  or  adverb;  what  then  is  an  adverb  ?  etc. 

In  this  way  the  adverb  is  first  taught  as  a  word  which  dis- 
tinguishes actions.  After  the  pupil  is  entirely  familiar  with 
this  idea,  the  use  of  the  adverb  as  distinguishing  the  qualities 
of  objects  should  be  presented.     This  may  be  done  by  com- 


246  METHODS    OF   TEACHING. 

'paring  two  qualities^  as  we  did  actions,  and  thus  obtaining  a 
list  of  words  which  distinguish  qualities.  The  pupil  is  then 
to  be  told  that  these  words  are  also  called  adverbs.  Let  the 
student-teacher  give  an  exercise  from  the  description. 

After  this  idea  is  clearly  in  the  mind,  the  office  of  the  ad 
verb  as  distinguishing  between  the  qualities  of  actions,  or  as 
limiting  an  adverb,  should  be  taught.  This  is  done  by  com- 
paring the  qualities  of  actions,  thus  the  quality  slowly  ma^'  be 
compared,  giving  us  very  slowly,  rather  slowly,  v^ore  slowly, 
etc.,  and  getting  a  list  of  words  which  distinguish  qualities  of 
actions,  and  telling  the  pupil  that  these  are  also  called  ad- 
verbs. The  manner  of  forming  adverbs  from  adjectives  by 
adding  like  or  its  contraction  ly,  thus,  sweet-like,  sweetly,  etc., 
may  also  be  shown.      Let  the  student-teacher  give  the  lesson! 

In  this  way  the  adverb,  in  its  three-fold  use,  may  be  under- 
standingly  taught.  With  the  more  advanced  pupils,  the 
question  ma}'  be  raised,  why  the  same  part  of  speech,  the  ad- 
verb, should  have  been  used  to  perform  these  three  offices, 
namely,  to  distinguish  actions,  qualities  of  objects,  and  quali- 
ties of  actions ;  and  wh}'  we  should  not  have  another  part  of 
speech  to  distinguish  qualities  of  objects  and  actions. 

Another  way  of  teaching  the  adverb  recommended  by  some 
teachers,  is  to  show  that  it  expresses  how,  when,  and  where, 
and  introduce  it  as  a  how,  when,  or  where  word;  but  the 
method  alread}' explained  is  preferred,  because  it  shows  the 
real  nature  and  office  of  the  word,  which  the  other  does  not. 

TJte  Pronoun. — We  teach  the  Pronoun  b}'  showing  the 
pupil  that  words  are  used  for  nouns.  We  get  a  list  of  such 
words  on  the  board,  drawn  from  actual  use  in  language,  and 
lead  the  pupils  to  call  them  for-nouns,  and  define  a  for-noun, 
as  a  word  used  for  a  noun.  Then  tell  them  that  there  is  a 
word,  pro,  derived  from  an  old  language,  wliich  means  the 
same  as /or,  and  lead  them  to  substitute  it  for  the  word  for, 
getting  the  word  pronoun;  and  then  lead  them  to  define  a  i)ro- 
noun;  and  continue  the  exercises  on  the  parts  of  speech. 


TEACHING   ENGLISH   GRAMMAR.  247 

Model  Lesson.— Teacher,  writing  on  the  board  the  sentence,  "Give 
John  John's  book,"  says,  How  else  may  this  be  expressed?  Pupil. 
Give  John /as  boolc.  T.  How  may  "Give  Mary  Mary's  book,"  be 
otherwise  expressed  ?  P.  Give  Mary  her  book.  T.  For  what  word  do 
we  use  his?  P.  For  John.  T.  What  part  of  speech  is  John?  P.  A 
noun.  T.  For  what  then  do  we  use  his  f  P.  For  a  noun.  T.  What  may 
we  call  words  which  we  use  for  nouns?  P.  For-nouns.  T.  What  then 
is  afor-nounf  P.  Kfor-noun  is  a  word  used  for  a  noun.  T.  If  we  use 
the  word  pro,  which  means /o/-,  in  place  of  for,  what  ^i\\  for-noun  be- 
come? P.  Pronoun.  T.  What  then  is  2i  pronoun?  P.  A  pronoun  is  a 
word  medfor  a  noun,  etc.     Keep  up  the  review  in  exercises  as  before. 

The  Conjunction. — The  Conjunction  may  be  taught  bj' 
leading  pupils  to  see  its  use  in  joining  words,  and  then 
leading  them  to  its  name  as  a  conjoining-ivord,  from  which 
they  can  be  led  to  the  term  conjunction.  Then  lead  to  the 
definition  and  give  an  exercise  on  all  the  parts  of  speech,  as 
previously  indicated.  For  these  exercises,  let  it  be  remem- 
bered, we  should  use  language  spoken  by  the  teacher,  or 
written  upon  the  board,  or  found  in  the  primary  reader. 

Modt'l  Lesson.— Teacher,  writing  on  the  board,  "John  can  read;  John 
can  write  " — ,  asks,  How  else  can  this  be  expressed  ?  Pupil  John  can  read 
and  write.  T.  What  word  is  used  to  join  rend  and  write  ?  P.  The  word 
and.  T.  What  kind  of  a  word  may  it  be  called?  P.  A  joining-word. 
T.  Yes,  or  a  conjoining -word.  T.  What  then  is  a  conjoin  irig-word  ?  P.  A 
conjoining- word  is  a  word  that  joins  or  unites  other  words.  T.  If  the 
word  conjunction  is  used  for  conjoining-word,  what  is  a  conjunction?  etc. 
In  a  similar  manner  we  may  show  that  the  conjunction  also  unites 
sentences. 

The  Preposition. — To  teach  the  Freposition,  we  show  the 
pupil  that  some  words  express  the  relation  of  objects,  and  that 
such  words  may  be  called  relation-words;  then  lead  to  a  defi- 
nition of  relation-words ;  then  introduce  the  term  preposition 
in  place  of  relation-word,  and  lead  to  a  definition  of  j)reposi- 
tion,  and  continue  the  exercises  as  before.  In  this  exercise, 
the  term  relation,  which  is  new  to  the  pupil,  is  best  explained 
by  using  it  in  the  lesson. 

Model  Lesson.— Teacher.  Standing  by  a  table  and  having  a  book  in  his 
hand,  What  object  is  this?    Pupil.  A  table.     T.  What  object  is  this?    P 


248  METHODS  OF  TEACHING. 

A  hook.     T.,  placing  the  book  on  the  table,  Where  is  the  book  now?    P. 

On  the  table.     T.  Where  is  the  book  now  ?     P.  Under  the 

table.     T.  Where  is  the  book  now  ?     P  Orer  the  table,  etc.        ^"^- , 

T.  Placing  the  biwk  on  tlie  table  again,  What  little  word        ^^^^ 

shows  the  ?rZ^7ft'(>/iof  the  book  to  the  table   now?  P.  On.        above. 

T.  What  little  word  shows  the  relation  of  the  b(X)k  to  the        beside. 

table  now?    P.  Under;  etc.     T.  Here  we  have  a  list  of 

words  which  do  what?    P.  Show  the  relation  of  objects.     T.  What  shall 

we  call  these  words  that  show  the  relation  of  objects?  P.  Belation-words. 

T.  What  then  is  a  relation- word?  etc.     T.  The  word  preposition  is  used 

for  relation-tpord  ;  what  then  is  a  preponition  f  etc. 

Ttie  Interjection, — The  Interjection  should  be  taught  as  a 
feeling-  or  emotion-ivord.  Ask  what  words  we  sometimes  use 
■when  we  feel  very  sad,  or  very  glad,  or  wlien  feeling  surprised, 
etc.,  and  get  a  list  of  words  like  oh,  ah,  aln.s^  hurrah,  pi^haw, 
etc.  Then,  since  these  express  feelings  or  emotions,  they  may 
be  cvi\\Q(\  feelinrj-  or  emotion-jvords.  Tlien  lead  to  the  defini- 
tion, etc.  At  last  lead  to  the  idea  that  they  are  interjected, 
or  thrown  in  between  other  words,  and  may  be  called  interjec- 
tions, and  lead  to  the  definition ;  and  then  drill  them  on  exer- 
cises on  all  the  parts  of  speech,  similar  to  the  manner  pre- 
viously suggested. 

II.  Properties  of  Parts  of  Speech. — By  the  Properties  of 
the  parts  of  speech  are  meant  those  things  which  belong  to  or 
are  peculiar  to  the  different  parts  of  speech.  They  include 
the  Number,  Person,  Gender,  and  Case  of  nouns  and  pro- 
nouns ;  the  Number,  Person,  Mood,  Tense  and  Voice  of  verbs ; 
and  the  C/)mparison  of  adjectives  and  adverbs.  These  proper- 
ties are  also  called  Inflections,  because  there  is  a  bending  or 
change  of  the  word  from  its  original  form  or  meaning. 

Idea  of  Property — The  first  thing  to  teach  under  Proper- 
ties, is  to  lead  a  pupil  to  a  clear  idea  of  what  is  meant  by  a 
property  of  a  part  of  speech.  Nine-tenths  of  the  pupils  in 
grammar  who  use  the  term  property,  never  stop  to  think  what 
it  means.  To  present  the  idea  of  propertxj,  take  two  objects, 
as  a  pencil  and  card.,  call  attention  to  their  qualities,  lead  to 


TEACHING    ENGLISH    GRAMMAR.  249 

the  idea  that  these  qualities  belong  to  the  objects,  lead  them  to 
tell  you  that  that  which  belongs  to  any  person  is  his  property, 
and  hence  those  things  which  belong  to  words  and  distinguish 
them  are  called  properties  of  those  words. 

Mo'lel  Leason.— Teacher.  What  are  these  objects?  Pupil.  K pencil  and 
card.  T.  Name  some  of  their  qualities.  T.  To  which  object  does  the 
quality  icliite  belong;  to  which  object  does  the  quality  black  belong? 
T.  The  things  which  belong  to  your  father— his  farm,  horse,  etc. — are 
called  his  what?  P.  His  property.  T.  What  then  may  we  call  tliose 
things  that  belong  to  objects?  P.  The  properties  of  objects.  T.  What 
may  we  call  the  things  which  belong  to  words?  P.  The  properties  of 
words.     T.  What  then  is  a  property  of  a  part  of  speech?  etc. 

We  can  teach  the  meaning  of  an  inflection  by  taking  a  word  like  abbot, 
which  expresses  a  man,  and  show  that  it  changes  to  abbess  to  express  a 
woman  ;  that  box  changes  to  boxes  to  express  the  plural ;  etc.  Then  lead 
them  to  see  that  such  changes  or  bendings  of  words  to  express  a  change 
of  thought,  are  called  bendings  or  inflections.  Let  the  student-teacher 
show  the  method  by  a  lesson. 

Properties  of  Nouns  and  Pronouns. — We  shall  first  con- 
sider the  properties  of  Nouns  and  Pronouns,  including  Num- 
ber, Person,  Gender,  and  Case. 

Number To  teach  Number,  we  lead  the  pupil  to  see  that 

words  have  one  form  for  one  thing  and  another  form  for  more 
than  one  thing  ;  and  then  since  one,  two,  three,  etc.,  are  num- 
bers, this  propert}'^  of  nouns  may  appropriately  be  called  the 
Number  of  nouns ;  and  the  pupils  may  be  led  to  define  it.  We 
then  lead  them  to  see  that  there  are  only  two  numbers,  since 
there  are  onh'  two  forms,  one  form  for  one  thing  and  another 
form  for  more  than  one  thing.  We  may  then  lead  them  to 
call  one  single  number  and  the  other  many  number,  from  which 
we  pass  to  singular  and  plural. 

We  may  then  lead  to  the  Rule  for  number,  by  leading  them 
to  see  that  we  sometimes  add  an  s  to  the  singular  and  some- 
times es,  and  sometimes  change  the  form  of  the  word,  in  form- 
ing the  plural. 

Model  Lesson. — Teacher.  What  have  I  in  my  hand?  Pw;n7.  A  book. 
T.  How  many  books  ?  P.  One  book,  T.  How  many  have  I  now  ?  P. 
11* 


250  METHODS   OF   TEACHING. 

Two  books.  T.  How  many  now  ?  P.  Three  books.  The  teacher  will 
then  write  on  the  board,  "I  have  one  book,"  "  I  have  two  books,"  "  I 
have  three  boolcs,"  etc.  T.  Which  is  the  noun  in  these  sentences?  T. 
How  many  forms  lias  it  ?  P.  Two  forms,  book  and  books.  T.  What  is 
its  form  for  one  thing?  T.  What  is  its  form  for  more  than  one  thing? 
T.  We  have  then  discovered  this  property  of  a  noun, — that  it  has  one 
form  for  one  thing  and  another  form  for  more  than  one  thing — let  us  see 
now  what  we  shall  call  this  property.  T,  What  are  one,  two,  three,  etc., 
in  arithmetic.  P.  Numbers.  T.  What  might  we  call  this  property  of  a 
noun  by  which  it  has  one  form  for  one  thing  and  another  form  for  more 
than  one  thing?  P.  The?mm/>erof  anoun.  T.  What  then  is  the  number 
of  a  noun  ?  P.  Number  is  that  property  of  a  noun  by  which  it  has  one 
form  for  one  thing  and  another  form  for  more  than  one  thing,  T.  Let 
us  now  see  how  many  numbers  nouns  have.  T.  How  man}'  forms  has 
the  noun  book  ?  P.  Tico  forms.  T.  How  manj'  numbers  then  are  there  ? 
P.  Two  numbers.  T.  If  there  were  three  forms,  one  form  for  one  thing, 
another  foim  for  two  things,  and  another  form  for  more  than  two 
things,  how  many  numbers  would  there  be?     P.  Three  numbers. 

T.  Let  us  see  now  what  we  shall  call  these  two  numbers.  T.  When  a 
horse  is  hitched  up  alone,  what  kind  of  a  harness  do  you  use?  P.  A 
single  harness.  T.  When  there  is  one  thing  alone,  then  what  may  you 
call  it?  P.  A  single  thing.  T.  What  may  we  then  call  this  number  of 
a  word  which  represents  a  single  thing?  P.  Single  number.  T  Very 
well  ;  that  is  right  ;  now  let  us  see  what  we  shall  call  the  other  numbt-r. 
T.  When  a  boy  has  a  "whole  lot"  of  marbles,  he  would  say  he  had  a 

great what  marbles  ?     P.  A  great  many  marbles.     T.  More  than  one 

thing  then  may  be  called  what  ?  P.  Mmig  tilings,  T.  This  number, 
then,  that  means  more  than  one,  maj'  be  called  what  number?  P. 
Many  number.  T.  What  are  the  two  numbers  then?  P.  Single  number 
and  many  number.  The  pupils  maj'  then  be  led  to  define  each,  and  sub- 
sequently the  words  singular  and  plural  may  be  introduced. 

They  may  then  be  led  to  see  that  in  words  like  hook  we  add 
s  to  form  the  plural,  and  state  it  as  a  rule.  They  may  then  be 
led  to  see  that  in  other  words,  as  in  box,  we  add  es  to  form 
the  plural,  and  state  it  as  a  rule.  Thej'  may  then  be  led  to 
see  that  we  sometimes  change  the  form  of  the  word  to  form 
the  plural,  as  man,  men,  o.r,  oxen.,  etc.  The  pupils  should  then 
be  drilled  on  forming  plurals;  and  also  make  a  list  of  the  per- 
sonal pronouns  classed -with  respect  to  number,  as  these  will 
be  needed  in  some  of  the  exercises  which  follow. 


TEACHING   ENGLISH    GRAMMAR.  251 

-  Taught  in  this  way,  the  pupils  will  see  that  though  there  are 
many  numbers  in  arithmetic,  there  are  only  two  numbers  in 
grammar,  since  there  are  onl^'  two  forms  of  words  to  distin- 
guish the  number  of  objects.  The}'  can  be  told  that  in  some 
languages,  as  the  Greek,  there  is  one  form  for  a  single  thing, 
another  form  for  two  things,  and  another  form  for  more  than 
two  things,  giving  three  numbers  in  grammar — the  singular^ 
the  dual,  and  the  jjlural.  „ 

I'erson. — To  teach  Person,  we  first  lead  the  pupils  to  see 
that  a  noun  may  represent  three  distinct  persons — the  person 
speaking ,  the  person  spoken  to,  and  the  person  spoken  of.  We 
tlien  lead  them  to  call  this  property  of  nouns  person ;  then  lead 
them  to  a  definition  of  the  person  as  that  property  of  a  noun 
b}-  which  it  represents  the  person  speaking,  the  person  spoken 
to,  and  the  person  spoken  of.  We  then  lead  them  to  see  that 
there  are  three  grammatical  persons,  and  that  they  are  appro- 
priatelj-  distinguished  as  first  person,  second  person,  and 
third  person.  To  do  this,  we  lead  them  to  see  that  the  first 
thing  necessary  for  something  to  be  said  is  a  jierson  speaking, 
the  second  condition  is  some  one  to  speak  to,  and  the  third  con- 
dition is  some  one  or  something  to  speak  of;  hence  the  name 
of  the  speaker  may  be  called  the  first  person,  the  name  of  the 
person  spoken  to,  the  second  person,  and  the  name  of  the  per- 
son or  thing  spoken  of,  the  third  person. 

The  pupils  should  then  be  required  to  point  out  the  person 
of  nouns  and  pronouns,  use  nouns  and  pronouns  of  a  given 
person  in  constructing  sentences,  and  be  drilled  on  exercises 
similar  to  those  already  suggested.  They  should  also  be  re- 
quired to  make  a  list  of  pronouns  arranged  according  to 
person. 

Let  the  student  of  this  book  be  required  to  translate  the 
above  description  into  an  inductive  lesson,  sucli  as  is  given 
under  the  previous  subjects.  The  following  three  sentences 
may  be  used  in  giving  the  lesson:  "I,  John,  am  Jiere;" 
"John,  come  here;"  "John  is  here." 


252  METHODS   OF   TEACHINQ. 

C(ise. — The  subject  of  Case  is  regarded  as  very  difficull  for 
young  pupils;  but,  if  properly  presented,  it  is  quite  readily 
understood.  We  should  first  teach  the  nominative  and  object- 
ive cases  together,  then  the  possessive  case,  and  then  the 
objective  case  after  the  preposition.  We  shall  describe  the 
lesson  briefly. 

The  teacher  will  write  on  the  board,  John  strikes  William, 
call  attention  to  the  action,  ask  who  does  the  action,  a\  ho 
receives  the  action,  then  ask  if  they  both  bear  the  same  ri  lo- 
tion to  the  action;  what  relation  John  bears  to  the  action, 
having  them  say  he  is  the  doer  of  it;  what  relation  William 
sustains  to  the  action,  leading  them  to  say  the  object  of  tiie 
action;  then  tell  them  that  this  property  of  words  sustaining 
ditferent  relations  to  an  action  is  called  Case,  and  lead  th«.m 
to  define  case ;  then  lead  them  to  call  John  the  doer  case  a.id 
William  the  object  case,  and  define  each  ;  after  which  he  van 
introduce  the  terms  nominative  and  objective. 

The  jyossessive  case  can  be  easily  taught  by  the  relation  of 
ownership  or  possession.  The  next  step  is  to  lead  to  the  dif- 
ferent case  forms  of  the  personal  pronouns.  A  list  of  tht'se 
should  be  made,  classed  according  to  case  ;  and  the  pupil  be 
drilled  on  them  until  he  knows  them  by  sight,  independently 
of  their  relation  in  the  sentence. 

The  next  step  is  to  teach  the  objective  case  after  the  prepo- 
sition. This  needs  especial  notice,  as  it  is  not  at  all  apparent 
to  the  learner  that  in  the  sentence,  "  He  gave  it  to  John," 
John  is  in  the  objective  case.  Indeed,  if  the  teacher  should 
take  the  two  sentences,  "  John  has  the  book,"  and  "  I  gave 
the  book  to  John,"  and  ask  what  case  is  John  in  the  first  sen- 
tence, and  then  what  case  is  John  in  the  second  sentence,  the 
pupils  would  say  nominative  in  both.  This  shows  that  it  ia 
not  evident  to  a  beginner  that  prepositions  require  the  object- 
ive case.  We  should,  therefore,  teach  the  objective  case  after  a 
preposition  by  the  use  of  the  pronoun.  Let  the  pupil  see  that 
in  the  sentence,  "  I  gave  the  book  to  John,"  we  cannot  say 


TEACHING   ENGLISH   GRAMMAR.  253 

"to /je,"  nor  "to  /*i.s,"  but  Jire  required  to  say,  "to  /im," 
which  is  the  objective  form;  hence  John,  which  is  represented 
by  him^  must  be  in  the  objective  case.  Let  the  pupil  then  l)e 
drilled  on  case  by  i)oiutiiig  out  the  case  of  words  in  sentences, 
constructing  sentences  with  given  cases,  etc.,  as  before  sug- 
gested. The  student-teacher  should  be  required  to  present 
this  description  in  an  inductive  lesson,  like  those  previously 
given. 

Gender. — Gender  is  easily  taught.  We  first  call  attention 
to  the  dirterence  of  .sej?  in  animals,  and  the  absence  of  sex  in 
other  objects.  We  then  show  that  some  words  change  their 
form  to  express  males  and  females, which  property  is  called  the 
gender  of  nouns  and  i)ronouns.  Then  lead  them  to  define  gen- 
der, to  see  that  there  are  two  genders,  since  there  are  two  sexes, 
and  lead  them  to  name  and  define  each.  Then  lead  them  to 
see  that  the  words  which  apply  to  objects  that  are  neither  male 
nor  female,  are  said  to  be  in  the  neuter  gender ;  and  also  that 
those  words  whicli  are  common  to  both  males  and  females  may 
be  said  to  be  in  the  common  gender.  The  main  point  of  difficulty 
is  to  distinguiiih  sex,  which  is  the  attribute  of  objects,  from  gender, 
which  is  a  property  of  words.  Give  abundant  exercises  as 
before  suggested.  The  student-teacher  may  be  required  to  give 
the  lesson  like  the  models  presented. 

Properties  of  the  Verb. — We  shall  now  show  how  to 
teach  the  properties  of  the  Verb  to  beginners  in  grammar. 
These  properties  are  Number,  Person,  Mode,  Tense,  and 
Voice.  The  properties  of  Number  and  Person  are  derived 
properties,  properties  which  the  verb  acquires  from  its  sub- 
ject. The  other  properties  are  intrinsic,  belonging  to  the 
verl)  per  se. 

Mode  of  Verbs. — To  teach  Mode^  write  on  the  board, 
"  John  studies  his  lesson,"  "  John,  study  3'our  lesson,"  and 
"  John  can  study  his  lesson."  Ask  which  sentence  declares 
the  action,  which  commands  it,  which  expresses  its  possibility, 
then  ask  which  part  of  speech  expresses  these  three  things. 


254  METHODS   OF    TEACHING. 

Ask  in  what  manner  the  verb  expresses  the  act  in  the  first 
sentence ;  have  them  say  it  simply  declares  the  act.  Ask 
in  what  manner  the  verb  expresses  the  act  in  the  second  sen- 
tence ;  requiring  them  to  say  it  commands  the  act ;  etc.  We 
thus  discover  the  property  that  a  verb  may  express  an  action 
in  different  manners  ;  then  inquire  what  we  may  call  this 
property  of  the  verb,  and  have  them  call  it  the  manner  of  the 
verb.  What  then  is  the  manner  of  a  verb  ?  If  we  use  the 
word  Mode,  which  means  the  same  as  manner,  what  shall  we 
call  this  property'  of  the  verb?  Ans.  The  Mode  of  the  verb. 
What  then  is  the  mode  of  a  verb  ?  etc. 

The  next  point  is  to  name  the  modes.  In  how  many  ways 
did  we  express  the  action?  How  many  modes  then  are  there? 
The  first  simpl}'  declares  or  indicates  the  act,  what  mode  then 
ma}'  we  call  it  ?  Ans.  The  declaring  or  indicating  mode. 
From  this  we  lead  to  the  declarative  or  indicative  mode. 
The  second  commands  the  act ;  lead  pupils  to  call  it  the  com- 
manding mode,  and  then  give  them  the  term  imperative.  The 
third  expresses  the  possibility  of  the  act ;  lead  them  to  call  it 
the  possible  mode,  and  then  give  them  the  term  potential^  as 
meaning  the  same  thing. 

The  subjunctive  mode  is  so  nearly  obsolete  that  it  need  not 
be  taught ;  and  the  infinitive  may  be  taught  by  its  form;  or, 
what  is  better,  be  called  an  infinitive,  and  not  regarded  as  a 
mode  of  the  verb.  The  participle  may  be  taught  in  the  same 
manner.  The  student-teacher  should  be  required  to  present 
the  method  of  teaching  mode  in  an  inductive  lesson. 

Tense  of  Verbs. — To  teach  Tense  we  first  call  attention  to 
the  kinds  of  time — present,  past,  and  future.  We  then  write 
on  the  board — "John  studies  grammar,"  "John  studied 
grammar,"  "John  will  study  grammar;"  and  ask  what  time  is 
expressed  by  each  form  of  the  verb,  and  thus  discover  that 
tlfe  verb  can  express  the  act  as  present,  past,  or  future.  We 
then  call  attention  to  this  property  of  a  verb  by  which  it  ex- 
presses different  kinds  of  time,  and  lead   the  pupils  to  call  it 


TEACniNQ   ENGLISH   GRAMMAR,  255 

the  time  of  the  verb.  We  then  introduce  the  word  iense^  mean- 
ing the  same  as  time  ;  lead  them  to  call  the  propert}^  the  tense 
of  the  verb,  and  then  lead  them  to  define  tense.  We  then  lead 
them  to  call  the  first,  present  tense,  the  second,  past  tense,  and 
the  third,  future  tense,  and  require  them  to  define  each. 

The  other  tenses  ma}'  also  be  easil}^  tanght.  Show  them 
that  have  studied,  since  it  denotes  the  act  as  completed  or 
perfected,  may  be  called  the  completed  or  perfect  teiise ;  and 
since  it  expresses  an  action  having  a  relation  to  the  present 
time,  it  may  be  called  the  present  perfect  tense.  Also  that 
had  studied,  since  it  denotes  an  act  completed  at  some  past 
time,  may  be  called  the  past  perfect  tense.  Also  that  shall  or 
will  haoe  studied,  since  it  denotes  an  act  completed  at  some 
future  time,  may  be  called  the  future  j)erfect  tense.  The 
tenses  of  the  potential  mode  may  be  taught  arbitrarily  by 
their  forms,  since  they  do  not  express  the  distinctions  of  time 
as  named.  The  student  teacher  will  put  the  above  in  an  in- 
ductive lesson, 

Nitmber  of  the  Verb. — The  Number  of  verbs  should  be 
taught  with  reference  to  the  number  of  their  subjects,  as  the 
verb  of  itself  has  no  number.  It  is  a  property  derived  from 
its  subject,  and  should  so  be  presented  to  the  learner. 

To  teach  the  number  of  verbs,  write  a  sentence  on  the  board, 
as  "  He  reads  the  Bible,"  and  under  it  "  They  read  the  Bible," 
and  ask  what  change  there  is  in  the  verb,  and  the  reason  for 
this  change.  Let  the  pupils  see  that  the  change  in  the  num- 
ber of  the  subject  causes  a  change  in  the  form  of  the  verb. 
They  thus  discover  a  property,  that  the  verb  changes  its  form 
when  the  subject  changes  its  number;  and  they  may  be  led  to 
call  this  property  the  number  of  the  vei-b.  Then  lead  them  to 
define  the  number  of  a  verb. 

Drill  the  class  on  the  singular  and  plural  forms ;  have  them 
point  out  the  forms  in  sentences,  construct  sentences  with 
given  numbers,  correct  mistakes  heard  in  conversation  with 
respect  to  the  number  of  the  verb,  etc.     Require  them  also  \.o 


256  METHODS   OF  TEACHING. 

derive  aud  state  the  rule  of  the  agreement  of  the  verb  with 
its  subject  in  number. 

Person  of  Verbs. — The  Person  of  the  verb  should  be 
taught  with  reference  to  the  person  of  its  subject,  as  the  verb 
in  itself  has  no  person,  but  derives  it  from  its  subject. 

To  teach  the  person  of  verbs,  write  on  the  board,  "He  reads 
a  book,"  and  under  it,  "  I  read  a  book,"  and  call  attention  to 
the  change  in  the  form  of  the  verb.  Then  lead  them  to  see 
that  the  subject  has  changed,  not  its  number  or  gender,  but 
its  person  ;  and  that  we  have  thus  discovered  a  property  of  a 
verb,  that  it  changes  its  form  as  its  subject  changes  its  person; 
and  that  this  property  may  appropriately  be  called  the  person 
of  the  verb.  Then  lead  them  to  define  the  person  of  a  verb  as 
that  property  by  which  it  changes  its  form  as  its  subject 
changes  its  person.  Then  drill  the  pupils  on  person,  as  pre- 
viously suggested. 

Voice  of  Verbs. — The  Property  of  Voice,  if  it  be  taught  at 
all,  may  be  presented  as  follows  :  Write  on  the  board,  "  John 
strikes  William,"  and  "  William  is  struck  by  John."  Lead 
the  pupils  to  see  that  in  the  first  sentence  the  verb  expresses 
the  subject  as  acting^  and  in  the  second  it  represents  the  sub- 
ject as  receiving  the  act.  We  thus  discover  a  property  of  a 
verb,  that  it  may  represent  its  subject  as  acting  or  being  acted 
upon.  This  property  needs  a  name;  what  shall  we  call  it? 
Call  their  attention  to  the  fact  that  we  express  things  with 
the  voice,  and  that  since  the  voice  is  a  way  of  expressing 
things,  this  property  of  verbs  by  which  they  express  the  act 
in  different  ways  may  be  called  voice. 

Then  lead  to  the  name  of  the  two  kinds  of  voice.  Since  the 
first  expresses  the  subject  as  active,  it  may  be  called  the 
active  voice.  Since  the  second  expresses  the  subject  as  re- 
r-eiving  the  action,  it  may  be  called  the  receiving  voice ;  or, 
since  the  word  passive  means  just  the  opposite  of  active,  and 
the  verb  expresses  its  subject  as  not  active,  but  passive,  this 
second  kind  of  voice  ma}'  be  called  the  passive  voice. 


.  TEACHING    ENGLISH   GRAMMAR.  257 

Comparison. — The  Comparison  of  adjectives  and  adverbs 
is  ver}'  easily  taught,  and  we  will  not  take  space  to  present  the 
subject  here.  Any  teacher  who  has  become  thoroughly  im- 
bued with  the  spirit  of  the  concrete  and  inductive  form  of 
instruction  used  in  the  previous  exercises,  will  have  no 
trouble  in  presenting  the  subject,  if  he  understands  it  himself. 

III.  Classes  of  Parts  of  Speech. — The  Classes  of  the 
Parts  of  Speech  should  next  be  presented.  It  might  be 
thought  that  these  should  have  preceded  the  Properties,  but 
in  several  cases  we  need  a  knowledge  of  the  properties  in 
order  to  make  the  distinction  of  classes.  In  actual  instruc- 
tion, they  should  be,  to  a  certain  extent,  combined,  which  is 
left  to  the  judgment  of  the  teacher.  It  is  more  convenient  to 
consider  them  separately  in  this  work.  Under  each  head  we 
will  describe  the  method  of  instruction,  but  the  student- 
teacher  should  be  required  to  present  it  in  the  form  of  an  in- 
ductive lesson.  The  author  of  this  work  does  not  consider 
his  pupils  as  prepared  to  teach  any  part  of  grammar  until 
the}'  can  present  an  inductive  lesson,  showing  just  how  the^' 
would  proceed  in  their  instruction. 

Classes  of  Nov  lis. — The  teacher,  b^'  appropriate  examples 
and  questions,  will  lead  the  pupil  to  see  that  some  nouns 
apply  to  particular  persons  and  things;  as,  John,  Mary,  Bos- 
ton, Washington,  etc.  Each  of  these  objects  has  its  parti- 
cular or  projier  name ;  and  hence  such  nouns  may  be  called 
proper  yiouns. 

Lead  the  pupil  to  see  also  that  many  similar  objects  have 
a  name  in  common ;  that  the  term  horse,  for  instance,  does 
not  distinguish  any  particular  horse,  but  is  a  term  common  to 
all  horses  ;  and  that  it  may  therefore  be  called  a  common 
noun.  Lead  them  in  the  same  wa}',  when  it  is  desirable,  to 
the  abstract  and  collective  noun,  and  also  to  the  classification 
in  respect  to  form, — Simple,  Derivative,  and  Compound. 

Classes  of  Verbs. — Verbs  may  be  classified  in  two  ways: 
I.  With  respect  to  their  object,  as  Transitive  and  Intransitive; 


258  METHODS   OF   TEACHING. 

2.  With  respect  to  their  ybrm,  as  Regular  and  Irregular.  The 
old  eUissification  into  active^  passive^  and  neuter,  is  being  dis- 
carded by  modern  grammarians.  It  might  be  well  to  retain 
the  term  neuter  for  the  verb  to  be,  and  regard  other  verbs  as 
active  and  passive,  instead  of  distinguishing  them  ])y  voice. 
The  passive  verb  seems  a  little  simpler  to  the  learner  than 
the  79a.s-sii;e  uotce  of  the  transitive  verb.  All  active  verbs  do 
not  express  action,  neither  do  verbs  in  the  active  voice. 

Transitive  and  Tntransitive. — To  teach  the  distinction  of 
transitive  and  intransitive,  lead  the  pnpil  to  see,  by  exatn|»k's 
and  questions,  that  sometimes  the  action  of  the  verl)  pnsse.-^ 
over  to  an  object,  and  sometimes  it  does  not ;  and  that  there 
are  thus  tivo  kinds  of  verbs.  Next  lead  them  to  see  that  the 
verb  in  which  the  action  passes  over  or  makes  a  transition  to 
the  object  may  be  called  a  transition  or  transitive  vc-rl),  and 
that  the  others  may  be  called  intransitive.  Tlien  drill  them  on 
transitive  and  intransitive  verbs,  as  found  in  sentences,  and 
also  in  constructing  sentences. 

Pupils  should  also  be  led  to  see  that  this  distinction  of  tran- 
sitive and  intransitive  is  not  an  absolute  one,  but  that  many 
verbs  are  used  in  both  ways.  Indeed,  there  is  hardly  a  tran- 
sitive verb  in  the  language  that  may  not  be  used  intransitivel}-, 

Regular  and  Irregular. — To  teach  the  distinction  between 
regular  and  irregular  verbs,  lead  the  pupil  to  see  that  some 
verbs  form  the  past  tense  b}-  adding  ed,  and  others  have  no 
regular  way  of  forming  it,  and  that  those  whicli  form  it  regu- 
larly may  be  called  regular  verbs,  and  that  those  which  form 
it  irregularly  may  be  called  irregular  verbs. 

Pupils  should  then  be  drilled  on  the  regular  and  irregular 
verbs.  A  list  of  the  irregular  verbs  should  be  presented  and 
carefully  studied  until  the  pupil  is  familiar  witli  their  proper 
forms.  Sentences  should  be  constructed  requiring  tlie  use  ot 
the  verb;  and  sentences  erroneous  in  this  respect,  corrected. 
Verbs  in  the  use  of  which  there  are  frequent  errors,  as  lay, 
lie,  sit,  sat,  prove,  drink,  etc.,  should  be  carefullj'  considered- 


TEACHING   ENGLISH   GRAMMAR.  259 

Infinitives There  are  two  forms  derived  from  the  verb, 

usually  called  the  infinitive  mode  and  the  participle,  to  which 
attention  is  briefly  called.  These  may  be  taught  by  the  form, 
arbitrarily  giving  them  the  names  applied  to  them ;  or  they 
may  be  taught  by  their  use  and  meaning.  The  pupil  may  be 
led  to  see  that  the  participle  participates  in  the  nature  of  a  verb 
and  adjective,  and  is  thus  appropriately  called  a  participle.  It 
may  also  be  shown  that  the  infinitive,  as  to  go,  having  n(j 
nominative,  is  unlimited  by  person  and  number,  and  is  thus 
indefinite  in  this  respect,  and  may  consequently  be  called  an 
infinitive,  which  means  unlimited.  It  may  also  be  shown  that 
the  participle  is  also  unlimited  in  person  and  number,  and  is 
thus  also  an  infinitive;  and  that  consequently  there  are  two 
infinitives,  the  verb  infinitive  and  the  participle  infinitive. 
The  pupil  should  also  be  led  to  see  that  there  are  two  partici- 
ples, the  present  and  the  past  or  passive. 

Classes  of  Prououus Pronouns  may  be  divided  into  five 

distinct  classes;  Personal,  Relative,  Interrogative,  Respon- 
sive, and  Adjective.  Authors  are  not  fully  agreed  in  this 
matter,  but  the  classification  given  is  convenient  and  as  cor- 
rect as  any  we  have  noticed. 

Personal  Pronouns. — In  teaching  Personal  Pronouns,  the 
teacher  will  lead  the  pupil  to  see  that  each  one  of  these  indi- 
cates by  its  form  whether  it  is  first,  second,  or  third  person, 
and  may  for  this  reason  be  appropriately  called  personal  pro- 
nouns. A  list  of  these  should  then  be  given,  and  the  pupil 
may  be  required  to  commit  them  to  memory.  The  student- 
teacher  may  present  an  inductive  lesson  on  the  subject. 

Relative  Pronouns. — A  Relative  Pronoun  may  be  taught  in 
two  ways  ;  etymologically  or  logically.  By  the  first  method, 
we  would  show  that  it  is  a  pronoun,  because  it  stands  for  a 
noun ;  and  that  it  is  a  relative  pronoun,  because  it  refers 
hack  or  relates  to  some  noun  already  named.  The  personal 
pronoun  can  be  used  independently  of  the  noun;  but  the  rela- 
tive pronoun  is  always  used  in  relation  to  a  given  noun. 


260  METHODS   OF   TEACHING. 

By  the  logical  method  we  would  teach  that  it  is  a  pronoun 
as  before ;  and  then  lead  tlie  pupil  to  see  that  it  is  a  relative 
pronoun,  because  it  connects  or  relates  the  clause  which  it  in- 
troduces to  some  previous  word  or  clause.  It  will  be  well  for 
the  student-teacher  to  put  both  methods  into  an  inductive 
lesson.  The  other  classes  of  pronouns  may  also  be  easily 
taught  in  a  similar  manner. 

IV.  Elements  of  Parsing. — The  pupil  should  begin  to 
parse  as  soon  as  he  begins  grammar.  As  he  leanis  each  part 
of  speech,  he  should  be  required  to  point  it  out  in  sentences. 
When  he  has  learned  some  of  the  properties,  he  should  also 
be  required  to  give  them  in  connection  with  the  parts  of 
speech.  This  is  the  kind  of  parsing  that  should  be  required 
in  the  Primary  Course.  It  should  be  informal,  and  often  con- 
sist merely  of  the  answering  of  questions  which  the  teacher 
maj'  ask  on  the  parts  of  speech  and  their  properties.  There 
should  be  no  formal  parsing,  that  is,  no  models  should  be  fol- 
lowed which  burden  the  memory  with  details.  The  main 
object  should  be  to  teach  grammatical  ideas  and  relations,  and 
not  grammatical  forms  of  expression.  To  introduce  these 
forms  of  parsing  too  early,  is  to  burden  the  mind  with  forms, 
and  thus  prevent  it  from  looking  at  the  grammatical  relations 
of  words. 

Y.  Elements  of  Analysis. — In  this  Primary  Course,  there 
should  also  be  some  instruction  in  the  elements  of  grrammat- 
ical  analysis.  This  instruction  should  be  presented  as  a  gen- 
eralization of  the  offices  of  the  parts  of  speech.  Pupils  should 
first  be  led  to  understand  the  subject  and  predicate  of  the 
sentence.  This  may  be  done  by  showing  that  the  verb,  which 
primarily  was  regarded  as  expressing  action,  is  used  in  ex- 
pressing an  assertion^  that  the  word  in  the  nominative  case  is 
the  subject  of  this  assertion,  and  may  be  called  the  subject  of 
the  sentence,  and  that  what  is  asserted  is  the  predicate.  It 
may  then  be  shown  that  a  collection  of  words  may  be  used  as 
the  subject,  and  a  collection  of  words  as  the  predicate 


TEACHING   ENGLISH   GRAMMAR.  261 

We  should  pass  next  to  the  subordinate  elements  of  the 
sentence.  The  pupil  may  be  led  to  see  that  the  adjectives 
which  originally  were  regarded  as  expressing  qualities,  mark 
out  or  limit  the  meaning  of  nouns,  and  may  be  called  limiting 
words.  We  should  then  pass  from  a  single  word  as  limiting  a 
noun  to  see  that  a  phra.se  and  a  clause  may  be  used  in  the 
same  manner,  and  may  then  also  be  regarded  as  limiting 
elements.  In  the  same  way  the  pupil  may  be  led  to  see  that 
the  phrase  and  clause  may  also  perform  the  office  of  an 
adverb,  etc. 

The  aim  of  this  instruction  is  to  teach  the  ideas  of  anal3^sis, 
and  lead  the  pupils  to  see  and  understand  these  logical  rela- 
tions :  but  no  formal  anal3'sis  should  be  required  of  them. 
They  may  be  required  to  answer  questions  and  point  out  ele- 
ments ;  but  they  should  not  be  required  to  commit  and  follow 
any  set  forms  of  statement,  as  is  properly  required  of  advanced 
pupils  in  grammar. 

VI.  False  Syntax. — Simple  examples  in  False  Syntax 
should  be  made  use  of  from  the  beginning.  Common  errors 
in  language  should  be  presented,  their  faults  pointed  out  and 
corrected.  Mistakes  heard  on  the  pla^'ground  should  be 
brought  in  and  corrected.  Pupils  should  be  encouraged  to 
watch  their  own  language  and  to  endeavor  to  correct  all  their 
mistakes.  No  formal  methods  of  correction  should  be  re- 
quired, however,  as  would  be  appropriate  for  an  advanced  class. 

YII.  The  Logical  Method. — After  the  pupil  has  attained  a 
fair  knowledge  of  the  parts  of  speech,  their  properties,  classi- 
fication, etc.,  with  the  elements  of  parsing  and  analysis,  he  is 
prepared  to  look  at  the  subject  of  grammar  from  the  stand- 
point of  thought ;  and  we  should  then  introduce  the  elements 
of  analysis  b}'  what  we  have  distinguished  as  the  Logical 
Method  of  teaching  grammar. 

In  the  Logical  Method  of  teaching  grammar,  the  sentence  is 
made  the  basis  of  the  instruction  :  the  method  beginning  with 
the  logical  analysis  of  the  sentence.     This  logical  analysis. 


262  METHODS   OF   TEACHING. 

instead  of  being  built  up  b3'  a  generalization  from  the  use  of 
words,  flows  from  the  sentence  as  expressing  a  thought,  and 
descends  from  the  various  elements  as  wholes  to  the  parts  of 
which  they  are  composed.  The  pupil  is  taught  to  look  at  a 
sentence  as  a  logical  whole,  and  to  study  the  logical  elements 
of  which  it  is  made  up.  Language  is  regarded  as  the  expres- 
sion of  thought,  and  the  structure  of  language  is  determined 
by  the  laws  of  thought. 

The  principles  of  Logic  are  thus  to  be  made  use  of  in  deter- 
mining the  principles  of  language.  Words  are  to  be  consid- 
ered not  merely  in  their  individual  meaning,  but  as  expressing, 
individually  and  collectively,  the  logical  relations  of  the  ele- 
ments of  thought. 

The  subject  and  predicate  are  regarded  as  expressing  con- 
ceptions of  the  mind,  the  one  being  compared  with  the  other, 
and  the  sentence  expressing  the  relation  betAveen  them.  In 
this  the}'  differ  from  nouns  and  verbs,  which  are  usually  re- 
garded not  as  expressing  the  mental  product,  but  as  the  names 
of  objects  and  actions.  The  subordinate  elements  are  regarded 
as  modifying  elements,  limiting  the  meaning  or  extent  of  the 
subject  and  predicate  conceptions.  In  this  they  differ  from 
the  adjective  and  adverb  etymologically  considered,  which 
express  qualities  of  objects  and  actions.  The  connective  ele- 
ments are  those  which  unite  the  other  elements  into  a  unity 
of  structure. 

Method  of  Teaching. — In  teaching  by  the  logical  method, 
we  should  begin  by  giving  pupils  a  clear  notion  of  an  idea  and 
a  thought^  and  also  of  a  sentence^  as  expressing  a  thought. 
We  should  then  lead  them  to  see  that  some  ideas  are  par- 
ticular and  others  are  general,  and  that  these  general  ideas 
embrace  many  individuals.  We  should  then  lead  them  to  see 
how  these  general  ideas  are  limited  in  their  extent  by  other 
elements  which,  in  comparison  with  the  principal  elements, 
va?Lj  be  called  subordinate  elements.  We  should  then  teacb 
them  to  see  the  different  classes  of  subordinate  elements,  etc 


TEACHING   ENGLISH    GRAMMAR.  268 

An  Idea We  ma}'  lead  pupils  to  a  knowledge  of  an  Idea 

by  having  them  look  at  an  object,  then  think  of  the  object 
when  not  looking  at  it,  noticing  the  product  in  the  mind,  and 
telling  them  that  this  mental  product  is  called  an  idea.  The 
exercise  we  suggest  is  as  follows : 

Model  Lesson.— Teacher.  Look  at  this  book.  Can  you  think  of  this 
book  when  you  do  not  see  it  ?  Can  you  Imagine  you  see  this  book  when 
your  eyes  are  closed?  Do  you  seem  to  have  a  picture  of  it  in  your 
mind?  Such  a  mental  picture  is  called  an  Idea.  What  then  is  the  dif- 
ference between  an  object  and  an  idea?  Is  the  object  in  the  mind?  Is 
the  idea  in  the  mind?  Where  is  the  object?  Pupil.  Outside  the  mind. 
T.  Where  is  the  idea?  P.  Within  the  mind.  Let  there  be  a  drill  also 
to  show  that  there  are  general  ideas  and  terms,  and  to  show  the  differ- 
ince  between  general  and  particular  ideas  and  names. 

A  Thought. — In  order  to  teach  a  T/jo^/gf/!.^,  have  the  pupils 
form  two  ideas,  compare  them,  and  think  the  relation  between 
them.  This  mental  product,  in  whicli  one  idea  is  affirmed  of 
another,  is  called  a  thought.  The  lesson  is  somewhat  as 
follows : 

}fodel  Lesson.— Teaclier.  Think  of  something,  as  a  robin.;  the  mental 
product  is  what?  Pupil.  An  idea.  T.  Think  of  something  else,  as  a 
bird  ;  the  mental  product  is  what  ?  P.  An  idea.  T.  Can  you  think  of 
any  relation  between  these  ideas?  csvn  you  unite  them  in  any  way?  P. 
Yes,  sir, — a  robin  is  a  bird.  T.  This  mental  product  is  called  a  thought. 
A  thought  is  the  relation  of  two  ideas  in  such  a  way  that  one  is  asserted 
of  the  other.  T.  Compare  the  two  ideas,  a  horse,  and  an  animal,  and 
affirm  the  one  of  the  other.  P.  A  horse  is  an  animal.  T.  This  is  also  a 
thought.  What  is  the  difference  between  an  idea  and  a  thought?  How 
many  ideas  are  necessary  to  a  thought  ? 

The  Sentence. — In  teaching  a  sentence,  we  merely  show 
that  it  is  the  expression  of  the  thought,  either  in  oral  or 
written  words.  Take  one  idea  or  object  of  thought,  and  affirm 
some  other  idea  or  object  of  thought  of  the  former;  write  the 
expression  on  the  board  ;  this  will  be  a  sentence.  Be  careful 
that  the  pupil  sees  that  such  combinations  as  nweet  apples, 
etc.,  are  not  sentences.  Teach  also  the  different  kinds  of  sep^ 
tences.     The  student-teacher  ma}-  give  the  lesson. 


264:  METHODS   OF   TEACHING. 

Subject  and  Predicate. — To  teach  the  Subject  and  Predicate, 
take  a  sentence,  call  attention  to  the  two  parts,  showing  that 
one  is  the  name  of  that  about  which  something  is  asserted, 
and  the  other  is  the  name  of  that  which  is  asserted  ;  lead  them 
to  call  the  first  the  subject,  from  the  subject  of  a  composition; 
and  the  latter  predicate,  because  the  teacher  saj's  that  is  its 
name. 

Model  Lesson. — Teacher.  In  the  sentence,  Boys  run,  how  maoy  parts 
are  there  ?  Which  is  the  part  about  which  something  is  said?  Which 
is  tlie  part  tliat  tells  what  is  said  of  boys  ?  Let  us  see  what  we  shall  call 
these  parts.  When  you  write  a  composition,  what  do  you  call  that  about 
whicli  yoa  write  t  Pupil.  The  Subject  of  the  composition.  T.  Very 
well;  what  shall  we  call  boys,  about  which  something  is  said  in  the  sen- 
tence, boys  run?  P.  The  subject  of  the  sentence.  T.  What  then  is  the 
subject  of  a  sentence  ?  The  word  ra/^s  does  what?  P.  Tells  or  asserts 
something  of  boys.  T.  What  may  it  be  called  ?  P.  The  telling  or  as- 
serting word.  T.  Well,  suppose  predicate  means  the  same  as  asserting 
word,  what  shall  we  call  runs  ?    P.  The  predicate,  etc. 

Subordinate  Elements. — The  Subordinate  Elements  may  be 
taught  somewhat  as  follows  :  Take  a  sentence  like  the  follow- 
ing; "Man}' bright  flowers  fade  quickly," and  have  them  show 
what  words  can  be  omitted  and  still  have  a  sentence;  and 
lead  them  to  call  the  necessary-  words,  ^^ou-ers  and  fade,  being 
more  important  than  the  others,  the  principal  elements.  The 
words  many,  bright,  and  quickly,  being  less  important,  are 
subordinate  in  rank,  and  may  be  called  subordinate  elements. 
Let  the  student-teacher  give  this  in  a  lesson. 

Limiting  Elements. — The  next  step  is  to  teach  that  a  sub- 
ordinate element  limits  the  meaning  or  extent  of  the  principal 
elements.  This  is  peculiar  to  the  logical  method  of  teaching 
grammar,  for  by  the  etymological  method,  the  adjectives  ex- 
press the  quality  of  the  objects,  and  the  adverbs  the  quality  of 
the  actions.  In  order  to  develop  the  idea  of  limitation,  use 
the  subject  first  in  its  full  meaning,  then  unite  a  word  with  it 
that  restricts  or  limits  it  to  a  portion  of  its  full  meaning,  and 
lead  the  pupil  to  see  that  the  oflace  of  a  subordinate  element 


TEACHING  ENGLISH   GRAMMAR.  265 

is  to  diraiuisli,  or  restrict,  or  limit  the  meaning  of  the  general 

idea  or  term. 

Model  fA's.son.  — Teacher.  When  I  s:iy,  "  Girls  study,"  how  many  girls 
may  I  iiieaa?  Pupil.  All  girls,  or  any  number  of  girls.  7'.  SuiJpose  I 
say,  "Good  girls  study,"  do  I  mean  all  girls?  P.  No,  sir,  only  a  part 
of  girls.  T.  What  word  is  it  that  restricts  or  liiyiits  the  meaning  o(  (jirls 
to  only  a  part  of  girls?  P.  The  word  good.  T.  What  kind  of  an  ele- 
ment may  I  caWgood  which  limits  the  meaning  of  girls?  P.  A  liiniting 
element.  T.  When  I  say,  "Good  girls  study,"  do  I  mean  any  particular 
studying?  P.  No,  sir.  T.  When  I  say,  "Good  girls  study  hard,"  do  I 
mean  any  particular  kind  of  studying  ?  P.  Yes,  sir,  hard  studying. 
T.  What  word  limits  the  meaning  of  study  to  hard  studying?  P.  The 
word  hard.  T.  What  kind  of  an  element  then  is  hard  ?  P.  A  limiting 
element. 

Kinds  of  Subordinate  Elements. — The  different  kinds  of 
subordinate  elements  are  words,  j<h rases,  and  clauses.  These 
may  be  taught  by  taking  an  exami)le  in  which  a  single  word 
limits  the  subject,  then  a  phrase  expressir^g  the  same  thing, 
and  then  expressing  the  same  with  a  clause. 

Model  Lesson.— Teacher f  writing  on  the  board,  "Normal  girls  study 
diligently,"  says.  What  word  limits  or  tells  the  kind  of  girls?  P.  The 
word  Normal.  T.  Suppose  I  write,  "Girls  of  the  Normal  study  dili- 
gently," what  now  expresses  the  kind  of  girls?  P.  The  words  of  the 
Normal.  T.  Such  a  collection  of  words  is  called  a  phrase.  Suppose  I 
write,  "Girls  who  live  at  the  Normal  study, "  etc.,  what  now  tells  the  kind 
of  girls?  P.  The  words  who  live  at  the  Normal.  T.  Is  there  a  subject 
or  predicjite  in  this  expression,  "  who  live  at  the  Normal  ?"  Is  it  then  a 
sentence  ?  Such  a  limiting  expression  is  called  a  clause.  What  kind  of 
words  limit  nouns?  P.  Adjectives.  T.  What  do  these  three  kinds  of 
elements  limit?  P.  They  limit  noun«.  T.  What  kinds  of  elements  then 
may  we  call  them?  P.  Adjective  elements.  T.  How  many  kinds  of  ad- 
jective elements  then  are  there?  P.  Three— (/'orcfs,  phrases,  and  clauses. 
In  a  similar  manner,  the  adverbial  elements  may  be  presented,  and  also 
the  objective  elements.     The  student-teacher  should  give  the  lesson. 

In  presenting  the  limiting  element,  we  have  regarded  it  as 
limiting  the  application  of  the  general  term:  we  mav  also 
present  it  as  limiting  the  extent  of  the  concept.  The  former 
method  is  in  accordance  with  Nominalism ;  the  latter  with 
Conceptualism. 
12 


266  METHODS    OF    TEACHING. 

III.  Methods  of  Teaching  Advanced  Grammak. 

After  the  pupils  have  attained  a  fair  knowledge  of  the  parts 
of  speech,  their  properties  and  classification,  with  the  elements 
of  parsing  and  analysis,  they  are  prepared  to  take  up  the  subject 
of  grammar  in  a  more  thorough  and  scientific  manner.  They 
are  then  prepared  to  consider  the  minutite  and  more  difficult 
points  of  the  sul)ject,  to  present  their  knowledge  in  a  complete 
and  systematic  form,  to  discuss  the  idioms  of  syntax,  to  learn 
and  apply  the  rules  of  construction,  and  see  the  logical  relation 
of  the  elements  of  language  as  determined  by  the  processes  of 
thought. 

This  higher  course _should  include  a  continuation  of  the  ety- 
mological exercises  of  the  primary  course,  the  committing  of  the 
principal  definitions  of  the  science,  a  full  course  in  parsing  and 
correcting  false  syntax,  a  complete  course  in  logical  analysis,  and 
the  grammatical  analysis  of  some  of  the  masterpieces  of  the  lan- 
guage. We  shall  speak  of  this  course  under  the  several  heads, 
the  Study  of  the  Text-book,  Formal  Parsing,  Correcting  False 
Syntax,  and  Grammatical  Analysis. 

I.  Study  of  Text-book. — A  text-book  should  now  be  placed 
in  the  hands  of  the  pupils,  and  regular  lessons  assigned  for 
them  to  prepare  for  recitation.  The  definitions,  as  given  in 
the  text-book,  unless  changed  by  the  teacher,  should  be  com- 
mitted and  recited  verbatim,  care  being  taken  that  they  are 
understood.  The  notes  and  observations  should  be  carefully 
studied,  and  their  sense,  not  the  exact  words,  be  required  to 
be  given  in  the  recitation. 

The  pupils  should  be  drilled  in  declensions,  comparisons, 
and  conjugations,  until  they  can  run  through  these  exercises 
with  rai)idity  and  accuracy.  They  should  also  be  drilled  on 
the  classification  of  the  parts  of  speech,  and  be  required  to 
write  logical  outlines  of  the  same. 

In  the  primary  course,  the  instruciion  was  inductive  ,  in 


TEACHING    ENGLISH    GRAMMAR.  267 

advanced  grammar  it  should  be  deductive.  There,  the  effort 
was  to  lead  the  pupil  to  understand  the  ideas  ;  here,  it  is  as- 
sumed that  the  pupil  already  understands  the  leading  princi- 
ples, and  is  able  to  acquire  other  ideas  and  to  recite  them. 
Of  course,  anj'  subject  not  understood  should  be  explained, 
inductively  or  deductively,  as  the  teacher  may  prefer. 

The  Rules  should  be  committed  to  memory  by  their  num- 
bers, so  that  they  may  be  readily  referred  to  in  parsing  and 
correcting  false  s^-ntax.  Notes  on  the  rules,  showing  their 
application  to  peculiar  cases  and  also  the  exceptions  to  them, 
should  be  thoroughly  studied.  Pupils  should  be  drilled  in 
the  peculiar  use  of  words,  the  idioms  of  construction  should 
be  explained,  and  all  the  more  difficult  parts  of  grammar  con- 
sidered. It  is  also  suggested  that  the  more  important  sub- 
jects be  taken  the  first  time  of  going  through  the  book,  leav- 
ing the  details  to  be  learned  on  the  review.  The  course,  if 
there  is  time,  should  reach  up  also  into  the  philosophical 
principles  of  the  subject,  and  embrace  the  laws  of  universal 
grammar. 

II.  Formal  Parsing. — In  connection  with  the  study  of  the 
subject  in  the  text-book,  there  should  be  regular  exercises  in 
Parsing.  This  is  an  old  exercise,  which  modern  analysis  has 
to  some  extent  thrown  into  the  background;  but  it  is  of  great 
value,  and  should  not  be  neglected  in  grammatical  instruction. 

Nature  of  Parsing. — Parsing  consists  in  naming  the  differ- 
ent parts  of  speech  in  a  sentence,  their  classes,  properties,  and 
relations.  It  is  a  consideration  of  the  grammatical  use  of 
words  in  sentences.  Parsing  maj'^  also  be  defined  as  the 
grammatical  description  of  words  in  sentences.  The  term  is 
derived  from  pars,  a  part.  It  is  an  exercise  that  should  be 
begun  as  soon  as  the  pupil  has  learned  a  few  of  the  elementary 
ideas  of  grammar,  and  should  be  continued  through  the  entire 
course  of  advanced  grammar. 

The  object  of  parsing  is  two-fold.  First,  it  affords  an  op- 
portunity to  appl}'  the  definitions,  classifications,  and  proper- 


?.Q8  METHODS   OF   TEACHING. 

Lies  which  have  been  loomed.  It  thus  aids  the  pupils  in 
becoming  familiar  with  the  definitions  and  rules  of  grammar, 
by  frequent  repetition  ;  and  teaches  them  to  express  their 
knowledge  in  a  systematic  manner.  Second,  it  requires  pupils 
to  examine  language  and  ascertain  the  nature  and  relation  of 
words  in  sentences;  and  this  not  only  gives  power  in„  the 
aualvsis  of  lano;ua2:e,  but  cultivates  the  habit  of  abstract 
thought.  The  object  of  parsing  should  lie  distinctl}-  under- 
stood, for  teachers  too  often  have  acted  as  if  the  end  of  studj^- 
ing  grammar  is  to  learn  to  parse ;  and  their  pupils  were  drilled 
upon  the  exercises  until  the^y  could,  with  propriety,  be  called 
"  parsing  machines." 

For  exercises  in  parsing,  we  should  first  use  the  sentences 
given  in  the  text-books.  As  the  pupils  advance,  we  should 
introduce  some  other  work  containing  good  specimens  of 
English  literature.  The  school  reader  may  be  conveniently 
used  as  a  "parsing  book."  A  little  work,  prepared  by 
Rickard  and  Orcutt,  called  Cla.^.s-book  of  Prose  and  Poetry^  is 
also  recommended.  Man}-  of  the  older  teachers  of  grammar 
used  such  works  as  Thomson's  Seasons,  Milton's  Paradise 
Lost,  Pollok's  Course  of  Time,  Cowper's  Task,  Pope's  Essay 
on  Man,  etc. ;  and  they  are  still  recommended  to  teachers  of 
advanced  classes. 

Forms  of  Parsing, — In  parsing,  beginners  should  not  be 
required  to  use  complete  and  logical  forms.  It  is  best  for 
them  to  go  over  the  words,  point  out  the  parts  of  speech,  and 
name  such  properties  as  they  have  studied,  and  then  answer 
such  questions  as  may  be  asked  by  the  teacher.  The  objec- 
tion to  using  forms  of  parsing  with  beginners  is,  that  pupils 
will  be  thinking  more  about  the  form  than  the  grammar ;  and 
will  fall  into  a  dull  routine  of  words  instead  of  thinking  of  the 
grammatical  relations.  Forms  of  parsing  should  not  be  intro- 
duced until  the  pupil  is  quite  familiar  with  the  fundamental 
ideas  of  grammar. 

In  the  advanced  course,  however,  pupils  should  be  required 


TEACHING   ENGLISH   GRAMMAR.  269 

to  use  a  definite  scheme  of  statement,  which  we  call  Forms  of 
Parsing.  Such  Forms  are  needed  for  several  reasons.  First 
they  economize  time  by  requiring  the  pupils  to  tell  what  the^ 
know  in  a  simple,  direct,  and  unhesitating  manner.  Second, 
they  facilitate  criticism,  as  we  can  very  much  more  readily 
detect  and  remember  a  mistake  when  the  pupil  has  a  regular 
order  of  statement,  than  when  he  mentions  the  properties  and 
relations  in  a  haphazard  sort  of  way. 

The  forms  of  parsing  should  be  simple.  The  complicated 
forms  which  we  sometimes  meet  with,  are  a  positive  disadvan- 
tage and  hindrance  to  the  pupil.  The  form  is  often  so  com- 
plex and  difficult  that  it  requires  nearly  all  the  mental  energy 
of  the  learner  to  follow  it,  and  leaves  but  little  for  the  grammar 
proper.  Pupils  often  make  mistakes  in  parsing,  not  because 
the}'  do  not  understand  the  grammatical  relations,  but  because 
some  part  of  the  form  slipped  from  the  memory.  Most  of  the 
corrections  made  in  the  class-room,  in  a  parsing  lesson,  it  is 
often  noticed,  are  with  respect  to  omissions  or  variations  of 
the  adopted  form. 

No  expressions  should  be  used  in  the  forms  that  are  not 
clearly  understood  by  the  pupils.  A  violation  of  this  rule  is 
a  ver}'  common  error.  Nine-tenths  of  those  who  use  such 
expressions  as  "prepositions  govern  the  objective  ease,"  "ad- 
jectives relate  to  nouns,"  "  adjectives  limit  the  nouns  to 
which  they  belong,"  "adverbs  qualify  or  vwdifij  verbs,  adjec- 
tives, and  other  adverbs,"  use  them  without  any  definite  idea 
of  their  meaning.  If  such  expressions  are  used,  require  the 
pupils  to  see  clearly  what  is  meant  by  "govern,"  "  relate  to," 
"  qualify,"  "  limit,"  "  modify,"  etc.  It  is  said  that  a  pupil,  on 
being  asked  something  about  the  expression  "  grammatical 
persons,"  as  used  by  an  author  in  defining  personal  pronouns, 
replied  by  naming  the  three  principal  grammar  teachers  of 
the  institution. 

The  full  form  of  parsing  should  often  be  dispensed  with. 
When  the  pupils  are  familiar  with  the  form,  it  is  a  waste  of 


270  METHODS   OF   TEACHING. 

time  and  patience  to  have  them  repeat  the  same  "lingo"  day 
after  da}'.  Let  a  portion  of  the  time  be  spent  in  having  them 
point  out  the  relations  of  words  and  answer  questions  upon 
some  of  the  more  important  and  difficult  things  connected 
with  the  sentence.  This  will  teach  them  to  think  grammar, 
and  not  merely  to  repeat  formulas. 

In  parsing,  we  should  generally  proceed  from  word  to  word 
in  the  order  of  their  arrangement  in  the  sentence.  Frequently, 
however,  the  teacher  ma}'  select  the  words  to  be  parsed,  as  it 
is  often  a  waste  of  time  to  parse  all  the  familiar  words.  The 
neglect  of  this  is  a  common  error  in  teaching  grammar.  We 
may  also  have  an  exercise  in  which  the  pupils  are  required  to 
parse  all  the  nouns  in  a  paragraph,  then  all  the  verbs,  then  all 
the  adjectives,  etc.,  in  their  order. 

Oral  Parsing. — We  shall  now  present  a  form  of  Oral 
Parsing.  Let  the  sentence  be,  "The  man  who  came  yester- 
day gave  me  a  pair  of  beautiful  sleeve-buttons."  The  form  of 
parsing  is  as  follows  : 

TJie  is  the  definite  article;  it  limits  man.     Rule. 

Man  is  a  common  noun;  in  the  masculine  gender,  third  person,  and 
singular  number;  it  is  used  as  the  subject  of  gave,  hence  it  is  in  the 
nominative  case.     Rule. 

Who  is  a  relative  pronoun;  its  antecedent  is  man,  lience  it  is  in  the 
masculine  gender,  third  person,  and  singular  number.  Rule.  It  is  used 
as  the  subject  of  came,  hence  it  is  in  the  nominative  case.  Rule.  It 
intro  luces  the  clause,  who  came  y  eater  day,  and  joins  it  to  man.     Rule. 

Came  is  an  irregular,  intransitive  verb;  principal  parts,  come,  came, 
coming,  come;  it  is  in  the  indicative  mode,  and  past  tense;  its  subject  is 
tcfio,  hence  it  is  in  the  third  person  and  singular  number.     Rule. 

Yesterday  is  an  adverb  of  time;  it  modifies  came.     Rule. 

Gave  is  an  irregular,  transitive  verb;  principal  parts,  gice,  gave,  giving, 
given;  it  is  in  the  active  voice,  indicative  mode,  and  past  tense;  its  sub- 
ject is  man,  hence  it  is  in  the  third  person  and  singular  number.     Rule. 

Me  is  a  persronal  pronoun;  in  the  common  gender,  first  person,  and  sin- 
gular number;  it  is  the  object  of  the  preposition  to  understood,  hence  it 
is  in  the  objective  case.     Rule. 

A  is  the  indefinite  ajiicle:  it  limits  pair.     Rule. 


TEACHING   ENGLISH   GRAMMAR. 


271 


Pair  IS  a  common  noun;  in  the  neuter  gender,  third  person,  and  sin- 
gular number;  it  is  the  object  oi  gam,  hence  it  is  in  the  objective  case. 

Rule. 

Of  is  a  preposition;  it  shows  the  relation  of  sleeve-buttons  to  pair.  Rule. 

Bedittiful  is  a  descriptive  adjective,  in  the  positive  degree;  it  modifies 
sleeve-b'ittons.     Rule. 

Sleece-buttonslsa.  compound  common  noun;  in  the  neuter  gender,  third 
person,  and  plural  number;  it  is  the  object  of  o/,  hence  it  is  in  the  object- 
ive case.     Rule. 

Written  Parsiufj. — There  should  be  forms  of  Written 
Parsing,  as  well  as  of  Oral  Parsing.  There  are  several  advan- 
tages in  written  parsing.  First,  it  enables  all  the  class  to 
be  reciting  at  the  same  time.  Second,  it  impresses  the  rela- 
tions of  words  by  seeing  them  written.  Third,  it  leads  to  an 
exactness  of  statement  that  the  oral  method  does  not  always 
attain.  This  written  ])arsing  can  be  on  the  blackboard  or  on 
paper.  The  oral  and  written  methods  can  be  combined  in  the 
same  recitation  to  great  advantage. 

We  present  also  a  form  of  written  parsing,  using  the  sen- 
tence given  below.  The  sentence  is  first  written  on  the 
blackboard  or  paper,  a  line  is  drawn  under  it,  and  the  words 
are  parsed  as  shown  in  the  form.  If  too  long  for  the  space 
assigned,  the  sentence  may  be  divided  as  in  ordinary  writing, 
room  being  left  between  the  parts  of  the  sentence  for  parsing 
the  words. 

The    man  who     came    yesterdayi  gave     me      a     pair    of    bracelets 
^acn      rp       iiv  at       jitv     pp     ia     en       p  en 

man     m     man     come        came        give     c     pair     n     pair         n 

3 

P 

gave 

o 


man 

who 

came 

en 

rp 

i  i  v 

m 

man 

come 

3 

m 

came 

s 

3 

coming 

gave 
n 

s 
came 

come 
i 

n 
man 

pa 

who 

3 

s 

yesterday 

gave 

at 

itv 

came 

give 

gave 

givins 

given 

a 

i 

pa 

man 

3 

s 

me 

a 

pair 

of 

PP 

i  a 

en 

P 

c 

pair 

n 

pair 

1 

3 

s 

s 

[io) 

gave 

o 

o 

It   is  thought   that  the  abbreviations  used  explain  them- 
selves.    If  they  do  not,  a  reference  to  the  forms  of  oral  pars- 


272  METHODS   OF   TEACHING. 

ing  will  make  them  clear.     For  a  fuller  presentation  of  the  sub- 
ject, see   Lyte's   Grammar  and    Composition,  published  by  D. 

Appleton  &  Co. 

Errors  in  Parsing. — Errors  in   Parsing  consist  of  three 

classes;  first,  errors  in  stating  the  part  of  speech  to  which  a 
word  belongs,  its  properties,  construction,  etc.;  second, errors 
of  expression  ;  third,  errors  in  tlie  form  of  parsing.  Some  of 
these  errors  are  the  result  of  a  want  of  knowledge  on  the  part 
of  the  pupil,  some  arise  from  carelessness,  and  others  are  due 
to  the  adoption  of  incorrect  forms  on  the  part  of  the  teacher. 
Errors  of  expression  include  the  mispronouncing  of  words, 
such  as  "nomitive"  for  "nominative,"  "singlar"  for  "singu- 
lar," etc.;  the  improper  omission  or  contraction  of  words, 
such  as,  "John  's  a  proper  noun"  for  "  John  is  a  proper  noun;" 
the  use  of  ungrammatical  or  awkward  expressions,  such  as 
"  nominative  case,  subject  of  is,"  "  nominative  case  governs 

the  verb,"  etc. 

The  forms  of  parsing  used  by  many  teachers  and  presented 
in  some  of  our  text-books,  contain  expressions  which  are 
awkward.  We  call  attention  to  a  few  of  these  expressions, 
suo-o-estino-  that  teachers  be  especially  careful  in  a  grammar 
recitation  to  teach  correctness  and  elegance  of  expression. 

Thus,  ''John  is  a  noun,  proper,^'  is  as  awkward  as  "John  is  a 
man,  aged,"  which  no  one  would  use  in  natural  expression. 
Again,  we  often  hear,  ''John  is  a  noun,  proper,  masculine 
gender;''^  which  really  says  that  John  is  proper,  is  masculine 
gender.  This  is  of  course  incorrect,  as  it  is  not  John  that  is 
proper,  but  the  noun  John. 

Pupils  often  use  the  expression,  "  according  to  rule.'''  This 
is  too  general  an  expression  ;  a  carpenter  builds  a  house  "  ac- 
cording to  rule,"  etc.  We  should  say,  "according  to  Rule  1," 
etc.;  or,  "  according  to  the  rule,"  keeping  the  voice  suspended, 
and  repeating  the  rule. 

Pupils  often  have  the  habit  of  using  the  word  and  immedi- 
ately after  naming  the  part  of  speech  ;  as,  "  The  is  an  article, 


TEACHING    ENGLISH    GRAMMAR.  273 

and  belongs,"  etc.  "O/is  a  preposition,  and  sliows  the  rela- 
tion," etc.  In  these  cases  there  are  two  distinct  tliouirhts,  the 
second  not  being;  a  continnation  of  tlie  first,  and  therefore  not 
to  be  coupled  with  it.  We  should  not  say,  "Mary  is  a  girl 
and  studies  her  lesson,"  but  "  Mary  is  a  girl;  she  studies  her 
lesson."  In  the  same  way  it  is  better  to  say,  "  The  is  an  arti- 
cle ;  it  belongs,"  etc. 

Pupils  often  use  the  expressions,  "  Third  person ,  it  is  spoken 
of,"  "  Second  person,  it  is  spoken  to,"  etc.,  thus  confounding 
the  noun  which  they  are  parsing  with  the  person  or  thing 
denoted  by  the  noun.  "Third  person,  it  denotes  the  person 
spoken  of,"  "  Second  person,  it  denotes  the  person  spoken 
to,"  etc.,  are  better  forms.  The  teacher  should  correct  these 
and  other  errors  which  he  meets  in  parsing,  for  the  language 
used  in  reciting  grammar  should  be  grammatical. 

III.  Grammatical  Analysis. — Within  a  comparatively 
short  period  of  time,  there  has  been  introduced  into  grammar 
a  logical  method  of  considering  the  sentence,  which  has  re- 
ceived the  name  of  grammatical  analysis.  It  has  done  much 
to  improve  the  study,  and  is  regarded  as  of  great  importance 
in  a  system  of  grammatical  instruction. 

Natuve  of  Analysis — In  the  et3'mological  studj'  of  gram- 
mar, words  are  considered  as  parts  of  speech,  and  classified 
into  nouns,  verbs,  etc.  These  individual  words  perform  cer- 
tain offices  in  the  construction  of  sentences  and  receive  their 
names  from  the  offices  which  they  perform.  By  and  by  it  is 
observed  that  collections  of  words  have  an  oflflce  in  sentences 
similar  to  many  of  the  parts  of  speech.  It  is  also  seen  that 
all  sentences  may  be  regarded  as  consisting  of  two  principal 
elements,  several  subordinate  or  modifying  elements,  and 
several  connective  elements.  The  discussion  of  a  sentence 
with  respect  to  all  these  elements  has  been  called  Grammatical 
Analysis. 

The  Elements — Grammatical  Analysis  regards  the  sentence 
as  consisting  of  three  classes  of  elements  ;  the  principal  ele- 
12* 


274  METHODS   OF   TEACHING. 

mentSj  the  subordinate  elements,  and  the  connective  elements. 
The  principal  elements  are  the  subject  and  predicate ;  the  sub- 
ordinate elements  are  the  adjective,  the  adverbial,  and  object- 
ive elements  ;  the  eonneetive  elements  include  the  preposition, 
the  conjunction,  the  relative  j^fonoun,  etc.  Besides  these, 
there  is  sometimes  an  element  having  no  relation  to  the  other 
elements,  called  an  independent  element.  All  sentences  are 
regarded  as  composed  of  these  elements,  which  elements  may- 
be represented  by  individual  words,  or  by  collections  of 
words. 

Importance  of  Analysis. — The  importance  of  grammatical 
analysis  in  the  study  of  language  can  hardly  be  overstated. 
It  gives  one  an  insight  into  the  principles  of  the  structure  of  a 
sentence  that  can  be  obtained  in  no  other  way.  It  lifts  the  sub- 
ject up  into  the  domain  of  logic,  and  enables  one  to  examine 
the  sentence  in  the  liijht  of  those  forms  of  thought  which  irive 
rise  and  shape  to  the  sentence.  It  enables  one  to  see  some  of 
the  functions  of  the  parts  of  speech  that  do  not  appear  in  the 
etymological  study  of  words.  Thus,  the  full  office  of  a  relative 
pronoun  cannot  be  appreciated  until  we  see  that  it  joins  a 
restrictive  clause  to  some  word,  and  the  idea  of  a  restrictive 
clause  is  given  by  analysis.  So  also  the  antecedent  term  of 
the  relation  of  a  preposition  is  not  alwa^'s  evident  until  we 
see  the  relation  of  the  modifying  phrase  which  it  introduces, 

Analj'sis  thus  becomes  a  powerful  instrument  in  the  hands 
of  the  grammarian  for  understanding  the  grammatical  rela- 
tions of  language.  Some  writers  go  so  far  as  to  say  that 
"grammar  can  be  successfully  studied  in  no  other  way." 
Dr.  Wickersham  sa3's  that  "  i)arsing  without  a  preceding 
anal3-sis  can  lead  to  but  a  ver^-  imperfect  knowledge  of  the 
organic  structure  of  sentences."  Prof.  Whitney  remarks, 
"  Give  me  a  man  who  can,  with  full  intelligence,  take  to  pieces 
an  English  sentence,  brief  and  not  too  complicated,  even,  and 
I  will  welcome  him  as  better  prepared  for  further  study  in 
other  languages  than  if  he  had  read  both  Caisar  and  Virgil, 


TEACHING    ENGLISH   GRAMMAR.  275 

and  could  parse  them  in  the  routine  style  iu  which  they  are 
often  parsed." 

Order  of  Parsing  and  Auoli/si.s — The  order  of  instruc- 
tion in  o-ranfmatieal  analysis  and  etymological  parsing  is  a  sub- 
ject upou  which  authors  are  not  agreed.  The  old  method  was 
to  beo-in  with  the  study  of  words;  and,  after  quite  a  full  knowl- 
edge  of  their  etymological  properties,  to  pass  to  the  analysis 
of  sentences.  A  large  number  of  recent  writers  maintain  that 
we  should  begin  with  the  sentence  and  present  the  logical  ele- 
ments before  we  teach  the  parts  of  speech.  ''  Since  the  gen- 
eral precedes  the. special,''  says  one  writer,  "the  treatment  of 
sentential  analysis  should  precede  any  exercises  in  parsing." 
Several  grammarians  endeavor  to  construct  their  text -books 
on  this  principle ;  but  most  of  them  drop  unconsciously  into 
the  etymological  consideration  of  words  before  presenting 
their  logical  use. 

It  is  our  opinion  that  grammatical  analysis  should  follow 
the  etymological  consideration  of  words.  There  are  several 
reasons  for  this  opinion.  First,  the  logical  elements  used  in 
analysis  are  really  a  generalization  of  the  uses  of  the  parts  of 
speech.  Grammatical  analysis  was  really  the  outgrowth  of 
grammatical  parsing,  by  a  generalization  of  the  etymological 
uses  of  words.  Thus,  we  should  understand  the  use  of  a  ivor^d 
as  an  adjectice  before  we  are  able  to  see  clearly  the  adjective 
use  of  a  phrase  or  a  clause.  It  thus  follows  the  order  from  the 
particular  to  the  general,  which  is  the  correct  order  for  primary 
instruction.  This  was  also  the  historic  order — parsing  was  in 
use  a  long  time  before  grammatical  anal^'sis  was  thought  of — 
and  the  historic  order  often  indicates  the  order  of  teaching. 

It  is  also  much  easier  to  begin  with  the  etymological  method. 
A.  pui)il  will  find  it  very  difficult  to  understand  the  use  of  the 
logical  elements  before  he  is  familiar  with  the  use  of  words  as 
parts  of  speech.  An  adjective  or  adverbial  element  will  hardly 
have  an}'  meaning  before  the  pupil  is  familiar  with  the  adjec- 
tive and  adverb.     The  idea  of  limitation,  which  is  the  analyt- 


276  JMETHODS    OF    TEACHIXa. 

ical  idea  of  an  adjective  and  adverbial  element,  is  much  more 
difficult  for  a  beginner  than  the  etymological  idea  of  adjectives  as 
expressing  qualities  of  oiijects  and  adverbs  as  expressing  qaalUies 
of  actions.  The  very  nomenclature  in  h)gical  analy«s  is  deriveil 
from  the  use  of  words  as  parts  of  speech.  The  two,  however, 
should  be  combined  as  early  as  possible,  as  the  analysis  will  often 
aid  the  parsing.  In  advanced  grammar,  analysis  may  even  pre- 
cede parsing. 

How  Tench  Analysis. — Logical  analysis  is  thus  Lest 
taught  to  beginners  by  a  generalization  from  tlie  nature  and 
use  of  the  ]>arts  of  speech.  Thus  it  may  be  seen  that  the 
noun,  which  was  primarily  a  name,  is  often  the  subject  of  an 
assertion,  and  that  the  verb,  which  was  primarily  an  action- 
word,  is  used  to  assert  or  predicate  something  of  the  subject 
It  may  then  be  shown  that  several  words  ma}'  express  the 
subject  of  the  assertion,  and  also  that  several  words  may 
express  the  predication.  Again,  it  may  be  seen  that  the 
adjective,  which  expresses  primarih'  a  quality  of  an  object, 
may  be  used  to  limit  the  meaning  of  the  noun,  and  also  that 
the  adverb  may  limit  the  meaning  of  a  verb  ;  and  rising  from 
this  idea,  we  may  see  that  a  collection  of  words  may  perform 
the  office  of  an  adjective  or  an  adverb,  and  thus  become  a 
limiting  element.  In  this  way  the  learner  may  reach  a  clear 
idea  of  the  logical  elements  of  sentences. 

It  is  recommended  that  the  elements  of  analysis  be  pre- 
sented as  early  in  the  course  as  pupils  are  prepared  to  under- 
stand it.  After  the  pupil  is  familiar  with  the  parts  of  speech 
and  their  genei'al  offices,  he  may  be  led  to  the  idea  of  a  subject 
and  a  predicate,  and  to  see  that  collections  of  words  perform 
the  same  office  in  the  construction  of  sentences  as  individual 
words.  He  may  thus  be  led  gradually  into  the  generalizations 
of  grammatical  analysis. 

At  a  certain  stage  of  grammatical  instruction  it  is  recom- 
mended that  a  purely  ''logical"  method  of  treating  the  sen- 
tence  be   presented,   the   pupil    being    taught   to   look   at   the 


TEACHING   ENGLISU   GRAMMAR.  277 

Structure  of  a  sentence  through  the  thought.  This  will  give 
him  additional  power  in  the  analysis  of  language,  as  it  enables 
him  to  look  at  the  grammatical  constructions  through  the 
medium  of  thought,  which  gave  it  existence  and  moulded  it 
into  its  present  form. 

He  may  be  led  to  a  clear  idea  of  ideas,  of  their  comparison 
giving  rise  to  judgments,  which  expressed,  give  the  ■proposi- 
tion ;  and  then  learn  to  distinguish  the  subject  and  predi- 
cate of  the  proposition.  He  may  then  pass  to  the  idea  of  the 
limitation  of  the  extent  of  a  concept,  and  thus  of  a  limiting 
element;  and  see  that  these  may  consist  of  words,  phrases, 
and  clauses.  In  this  way  he  can  reach  the  details  of  analysis, 
passing  down  until  it  meets  its  complement,  parsing,  in  the 
etymological  use  of  the  individual  words  of  which  a  sentence 
is  composed. 

This  logical  analysis  may  be  presented  less  subjectively  by 
regarding  the  words  as  denoting  objects,  classes,  etc.,  in- 
stead of  ideas;  and  the  subordinate  elements  as  pointing  out 
or  distinguishing  particular  individuals  or  classes,  instead  of 
limiting  the  ideas;  or  as  limiting  the  application  of  the  term 
rather  than  limiting  the  idea  or  concept.  This  latter  method 
is  more  objective  than  the  former  and  probably  a  little  sim- 
pler; but  it  does  not  seem  so  closely  related  to  the  laws  of 
thought  as  the  logical  method  previously  described.  It  would 
no  doubt  be  more  acceptable  to  the  "nominalist"  than  the 
former  method. 

Methods  of  Analysis The  logical  analysis  of  a  sentence 

may  be  presented  in  two  distinct  ways,  which  may  be  distin- 
guished as  the  analytic  and  synthetic  forms.  By  the  former 
method,  we  first  name  the  sentence  as  a  whole,  then  sei)arate 
it  into  its  parts,  naming  the  entire  subject  and  the  entire 
predicate,  then  pass  from  the  entire  subject  to  the  simple  or 
grammatical  subject,  and  name  its  limitations,  and  proceed 
to  an  analysis  of  each  of  those  elements;  and  then  analyze  the 
predicate  in  the  same  manner. 


278  METHODS   OF   TEACHING. 

B3'  Uie  other  method,  we  first  name  the  sentence  as  a 
whole,  then  name  the  simple  subject,  then  the  subordinate 
elements  which  limit  it,  giving  an  analysis  of  these  stibordi- 
nate  elements,  then  put  the  simple  subject  and  its  subordinate 
elements  together  and  name  the  com[)lete  or  logical  subject ; 
and  then  proceed  in  the  same  manner  with  the  predicate, 
passing  from  the  simple  to  the  entire  or  logical  predicate. 

These  two  methods  are  very  nearly  opposite  in  form,  though 
they  do  not  differ  in  spirit.  Some  teacliers  prefer  one  method 
and  some  the  other,  though  it  is  difficult  to  tell  which  is 
preferable.  The  synthetic  is  probabl}'  a  little  easier,  as  it 
gives  a  little  more  time  to  see  what  the  full  subject  or  predi- 
cate of  the  assertion  is.  It  should  be  noticed  that  the  syn- 
thetic forui  of  statement  is  just  as  much  an  exercise  in  logical 
analysis  as  the  anal3'tic  method  ;  the  sjjirit  is  the  same,  the 
only  difference  is  in  the  form  or  order  of  statement. 

JToruis  of  Analysis. — We  shall  now  present  some  forms 
for  oi'al  and  written  analysis.  The  necessity  of  such  forms 
is  clear  from  what  lias  been  said  in  regard  to  forms  for  oral 
and  written  parsing.  The  forms  for  analysis  should  possess 
the  same  attributes  as  those  for  parsing  ;  that  is,  they  should 
be  simple,  clear,  and  logical.  The  forms  presented  are  nearly 
the  same  as  those  used  by  Prof.  E.  O.  L^-te  in  his  Grammar 
and  Composition.  To  illustrate,  we  take  the  sentence  used  to 
represent  the  forms  of  parsing, — "  The  man  who  came  yester- 
daj',  gave  me  a  pair  of  beautiful  sleeve-buttons." 

Ordl  Analysis. — This  is  a  complex  declarative  sentence.  Man  is  tlie 
subject;  it  is  limited  by  the,  an  article,  and  'r/m  cuine  i/esterdai/,  au  ad- 
jective clause;  irJio  is  tlic  subjccl  of  the  claiise  ;  it  is  used  also  as  a 
subordinate  connective  ;  nnne  is  the  predicate  ;  it  is  limited  by  i/es- 
terdny,  an  adverb.  Hare  is  the  predicate  of  the  sentence;  it  is  limited 
by  to  me,  an  adverbial  phrase  ;  to,  understood,  is  a  preposition,  connect- 
ing gave  and  me  ;  me  is  the  object  of  to;  gave  is  also  limited  by  pair,  its 
object  ;  pair  is  limited  by  a,  an  article,  and  of  sleere-huttons,  an  adject- 
ive phrase;  <>/ connects  pi  (tV  and  sleem-battons  ;  sleeve-buttofis  is  limited 
hi'  beautiful,  an  adjective. 


TEACHING   ENGLISH   GRAMMAE.  279 

WRITTEN  ANALYSIS,  OR  OCTIaLNE. 


man 

« 

The"-^ 

adj 

who » " 

cameP 

yesterday  **• 

gave 

p 
(tojPme" 

adv 

pair" 

o(P  sleeve-buttx)ns» 

"''■'■     beautiful"* 

Some  teachers  prefer  a  slightly  different  method  of  stating 
the  analysis.  Thus,  instead  of  saying,  "it  is  limited  by  who 
came  yesterday,  an  adjective  clause,"  they  say,  "  it  is  limited 
by  who  came  yesterday,  a  clause  used  as  an  adjective."  Still 
another  method  is,  "  it  is  limited  b}'  the  adjective  chiuse  who 
came  yesterday,''''  which  we  like  about  as  well  as  the  model  we 
have  given.  It  is  a  question  whether  we  should  name  the  parts 
of  speech  in  analysis;  thus,  whether  we  should  say,  "it  is  lim- 
ited b}'  the,  an  article,"  or  rather,  "it  is  limited  by  the,  an  ad- 
jective element,"  or  "by  the  adjective  element  the.''''  Logical 
analj'sis  may  be  complete  without  mentioning  or  even  Ivuowing 
the  parts  of  speech  ;  though  it  is  convenient  to  use  the  name 
of  the  part  of  speech  when  the  element  is  a  single  word. 

Mixed  Method. — There  is  also  a  method  of  disposing  of 
sentences  that  combines  analysis  and  an  abridged  method  of 
parsing,  which  may  be  called  a  mixed  method  or  grammatical 
de'icription.  This  is  a  valuable  practical  method,  and  is  re- 
commended for  the  use  of  pupils  who  are  familiar  witli  the 
el "iments  of  parsing  and  analysis.  The  method  in:iy  l)u  illus- 
trate'd  with  the  sentence,  "  The  man  whom  I  saw  yesterday 
lives  in  Boston."  TVe  present  it  in  two  different  foiin.s  ;  oiu' 
b^ing  somewhat  synthetic  and  the  other  somewhat  asialytic. 

Firat  Form. — The  man  trhom  I sair  i/extenJtii/  Uccs  in  Boxton.  This  is  a 
^•implex,  declarative  sentence.  The  is  an  article  ;  it  is  used  to  iiioditV 
•aaM.     Man  is  a  noun;  it  is  used  as  the  subject  oolites.      Wnun  is  a  rcU- 


280  METHODS   OF   TEACHING. 

tive  pronoun,  its  antecedeut  is  man;  it  is  used  as  tlie  direct  object  of 
saiD  ;  it  introduces  the  clause  iclinyn  I  saw  &n&  joins  it  to  man.  Whom 
I  saw  is  a  clause  used  as  an  adjective;  it  modifies  man.  /is  a  pronoun;  it 
is  usod  as  tlie  subject  oi saw.  Saw  is  a  verb;  its  subject  is  /.  Yesterday 
is  an  adverb;  it  is  used  to  modify  aaw.  J  is  the  subject  of  the  clause,  and 
saw  wlujin  is  the  entire  predicate.  Liccs  is  a  verl);  its  subject  is  man.  In 
is  a  preposition;  it  is  used  to  introduce  the  phrase  m  i^o^^iort,  and  join 
it  t«  lices.  In  Boston  is  a  phrase  used  as  an  adverb;  it  modifies  lives. 
Boston  is  a  noun;  it  is  used  as  the  object  of  in.  The  man  whom  I  saw 
yesterday  is  the  entire  subject  of  the  sentence,  and  lives  in  Boston  is 
the  entire  predicate. 

Second  Form. — The  man  whom  I  saw  lives  in  Boston,  is  a  complex  sen- 
tence. The  man  lives  in  Boston  is  the  principal  clause,  and  whom  I  saw 
is  the  subordinate  clause.  The  man  whom  I  saw  is  the  entire  subject; 
and  lices  in  Boston  is  the  entire  predicate.  3Ian  is  a  noun  used  as  subject 
of  lices.  The  is  an  article,  used  to  modify  7nan.  Whom  I  saw  is  a  clause, 
used  as  an  adj  ecti  ve  to  modi  fy  imm.  /  is  a  pronoun,  used  as  subj  ect  of  saw. 
Saw  is  a  predicate  verb;  its  subject  is  7.  Whom  is  a  relative  pronoun;  as 
a  pronoun  it  is  used  as  object  of  saw,  as  a  relative  or  subordinate  connect- 
ive it  introduces  the  clause  whom  I  saw,  and  joins  it  to  man.  Lices  is  a 
predicate  verb;  its  subject  is  man.  In  Boston  is  a  phrase  used  as  an 
adverb  to  modify  lices.  In  is  a  preposition  used  to  show  the  relation  of 
Boston  to  Vices.    Boston  is  a  noun  used  as  the  object  of  in. 

Errors  in  AnalysL^. — Errors  in  analysis  consist  of  two 
classes:  first,  errors  in  stating  the  classification  and  elements 
of  a  sentence;  and  second,  errors  of  expression.  Errors  of 
expression  include  the  misuse  of  terms,  such  as  clause  for 
phrase,  sentence  for  clause,  or  member;  the  needless  repeti- 
tion of  terms,  such  as  "of  which,"  the  use  of  unnecessary 
terms,  such  as  "elements  of  the  second  class,"  "  elements  of 
the  third  class,"  etc.  A  very  common  error  in  forms  of  analy- 
sis is  the  use  of  long  and  involved  sentences  in  which  tlie 
thought  becomes  obscured  in  the  construction.  The  different 
points  should  be  simply  and  directly  stated. 

In  written  analysis,  the  commonest  errors  are, — errors  of 
arrangement,  and  errors  in  writing  the  abbreviations.  The 
teacher  will  be  careful  to  guard  against  the  following  mis- 
takes :  Drawing  the  lines  too  long, or  in  an  oblique  direction; 


TEACHING   ENGLISH   GRAMMAR.  281 

failing  to  write  the  modifying  words  and  the  connectives  in 
the  proper  places  ;  writing  the  predicate  too  far  below  the  sub- 
ject; failing  to  write  the  proper  abbreviations  in  the  right 
place,  and  in  a  smaller  hand  than  that  used  in  writing  the 
sentences. 

Diagrams  for  Analysis. — Several  efforts  have  been  made 
to  devise  some  form  of  written  analysis  which  will  'picture  the 
grammatical  relations  to  the  eye.  The  most  prominent  of 
these  methods  is  that  of  Prof.  Clark,  called  the  "diagrammat- 
ical method,"  given  in  Clark's  grammar.  A  method  of  graphic 
analysis  that  looks  well  upon  the  board  is  that  given  in  Reed 
and  Kellogg's  grammar.  It  is  supposed  that  such  a  represent- 
ation aids  the  learner  in  grasping  the  grammatical  relations 
of  words,  on  the  principle  that  the  abstract  idea  ma}^  be  seen 
through  the  pictured  form.  The  objection  to  some  of  these 
methods  is  that  it  often  requires  more  ingenuit}'  to  prepare  the 
diagram  than  to  understand  the  grammatical  relations.  If 
used  at  all,  they  should  not  be  made  prominent,  or  a  pupil  will 
become  so  dependent  upon  them  that  he  will  be  unable  to  see 
the  grammar  of  a  sentence  except  through  the  medium  of  a 
diagram.  Used  occasionally  for  illustration,  they  may  be  of 
value  to  the  student ;  but  when  employed  as  a  regular  method 
of  recitation,  we  believe  them  to  be  objectionable. 

IV.  CoRKECTiNG  False  Syntax. — By  False  Syntax  we  mean 
constructions  in  language  which  violate  the  laws  and  usages 
of  grammar.  The  principle  upon  which  the  correction  of 
false  syntax  is  based  in  teaching  grammar,  is  that  we  learn 
the  true  by  seeing  the  false ;  as  the  Spartans  taught  their 
children  temperance  by  showing  them  the  silly  actions  of  the 
Helots  when  intoxicated. 

The  object  of  correcting  false  s}- ntax  is  twofold.  First,  it 
gives  a  clearer  knowledge  of  the  rules  of  syntax,  and  their 
application  to  language  ;  second,  it  impresses  the  correct  form 
of  the  sentence,  and  leads  us  to  avoid  the  errors  with  which 
we  are  thus  made  familiar.     Its  importance  in  a  course  of 


282  METHODS   OF   TEACHING. 

grammatical  instruclion  is  thus  apparent :  it  aids  tlie  pupils 
in  obtaining  a  more  thorough  knowledge  of  the  rules  of  gram- 
mar, and  trains  them  to  acquire  correct  habits  in  the  use  of 
language. 

The  exercises  selected  should  in  the  main  be  such  as  actu- 
ally occur  in  conversation  and  writing,  and  not  all  sorts  of 
impossible  eruors.  It  is  hardly  worth  while  to  manufactui'e 
errors  such  as  may  never  be  heard  or  seen  in  language,  as 
enough  actual  mistakes  ma}-  be  found  to  illustrate  every  rule. 
The  errors  of  common  conversation  should  be  made  especially 
prominent,  as  "  Please  let  John  and  I  go  home,"  "  Who  did 
you  see,"  "  Who  were  3'ou  with,"  etc.  We  should  also  have 
examples  of  the  mistakes  involving  the  nicer  distinctions  of 
grammar,  as  the  use  of  shall  and  ivill,  the  forms  of  the  irreg- 
ular verbs,  and  the  popular  tendencies  to  depart  from  the  strict 
rules  of  s^'ntax.  The  slips  of  eminent  writers  will  be  found 
useful  to  impress  upon  the  minds  of  pupils  the  necessity  of 
being  careful  in  writing. 

The  exercises  in  false  sj-ntax  should  be  used  in  connection 
with  parsing  and  analysis.  They  may  be  given  along  with  the 
etymological  exercises  of  the  book  after  the  correct  forms  have 
been  explained.  Some  authors,  as  Goold  Brown,  give  a  large 
collection  of  such  exercises  under  the  detailed  discussion  of 
the  rules  of  syntax,  which  is  a  ver}'  convenient  method  of  con- 
sidering the  subject.  Some  teachers  recommend  that  the  ex- 
ercises be  graded,  following  the  order  of  the  sentence,  proceed- 
ing from  the  simplest  form  of  the  sentence  in  the  first  step  to 
the  most  complicated  form  in  the  last  step ;  but,  though  such 
a  treatment  would  be  logical,  it  is  a  question  whether  it  would 
possess  any  practical  value. 

Forms  of  Corrccfhu/. — With  beginners,  as  already  stated 
in  the  primary  course,  no  special  form  is  to  be  used  in  recita- 
tion, the  object  being  to  call  attention  to  the  error  and  correct 
the  practice.  With  the  advanced  course,  some  definite  fonn 
should  be  used  by  the  pupils  in  recitation.     This  form,  as  in 


TEACHING   ENGLISH   GRAMMAR.  283 

parsing  and  anal3'sis,  should  be  as  simple  as  is  consistent  with 
a  clear  and  complete  statement  of  the  nature  of  the  error  and 
its  correction.  The  teacher  ma}'  have  his  pupils  use  a  full 
form  until  they  are  familiar  with  it,  and  then  pass  to  an 
abbreviated  form.  Frequentlv  in  the  recitation,  all  form 
should  be  dispensed  with,  the  pupil  mercl}'  being  required 
to  state  the  error  and  the  correction.  We  present  several 
forms,  as  suggested  by  Prof.  Byerly,  and  used  by  him  in  his 
classes. 

First  Form. — The  first  method  of  correcting  false  syntax 
embraces  five  distinct  things:  1.  The  pupil  states  that  the 
sentence  is  incorrect ;  2.  He  shows  wherein  the  rule  is  vio- 
lated ;  3.  He  quotes  the  rule  violated  as  authority  ;  4.  He 
states  what  should  be  omitted,  supplied,  substituted,  or 
changed ;  5.  He  gives  the  sentence  in  its  correct  form.  To 
illustrate,  take  the  sentence,  "  Who  went  ?     Us  girls." 

Illustration.— "Who  went?  Us  gtrW  This  sentence  is  incorrect; 
because  "us,"  a  pronoun  in  t!ie  objective  case,  is  used  as  the  subject  of 
"went";  but  according  to  Rule  I.,  A  noun  or  a  pronoun  used  as  the 
subject  of  a  finite  verb  must  be  in  the  nominative  case  ;  therefore,  instead 
of  "us,"  "we"  should  be  used;  and  the  sentence  should  be,  "Who 
went?    We  girls." 

Second  Form. — Another  method  is  that  which  gives  the 
result  first  and  the  reamn  afterward.  It  differs  from  the  first, 
as  the  last  two  steps  of  that  are  made  the  second  and  third  in 
this.     We  illustrate  with  the  same  sentence. 

Illustration.— "WJio  went f  Us  girls."  This  sentence  is  incorrect; 
instead  of  "us,"  "  we"  should  be  used  ;  and  the  sentence  should  be,— 
"  Who  went?  We  girls";  it  is  incorrect  because  "us."  a  pronoun  used 
as  the  subject  of  "  went"  understood,  is  not  in  the  nominative  case  ;  bnt 
according  to  Rule  I.,  etc. 

Other  Forms. — Other  methods,  less  formal  than  these,  may 
also  be  used.  Thus,  we  may  navie  the  error,  then  the  c<)?-rec. 
tion,  and  then  give  the  reason  for  the  correction  by  q noting 
the  rule.     Another  form,  which  we  should  often  use,  is  that 


284  METHODS    OF   TEACHING. 

m  which  the  pupil  reads  the  sentence  as  given,  and  then 
simply  reads  it  as  corrected. 

Errors  in  Corrcctiug. — There  are  several  erroneous  ex- 
pressions to  which  pupils  are  liable  in  correcting  false  syntax, 
which  should  be  avoided.  First,  the  pupil  should  not  be  al- 
lowed to  say  "  'us'  should  be  changed  to  'we'  ",  as  that  cannot 
be  done.  Second,  the  pupil  should  not  say  "  The  sentence 
should  read";  but  rather  "the  sentence  should  be." 

Written  Exercise. — There  may  also  be  a  written  exercise 
in  correcting  false  syntax.  The  teacher  may  dictate  the  sen- 
tences and  have  them  written  on  paper  or  on  the  blackboard, 
and  then  have  them  corrected  by  drawing  a  line  under  the 
incorrect  word  and  writing  the  correct  word  below  it.  Or  the 
teacher  can  write  several  sentences  on  the  board,  numbering- 
them  in  the  order  in  which  the^'  are  written,  and  require  the 
pupils  to  write  them  correctly,  indicating  them  by  the  proper 
numbers.  "When  written  on  paper,  they  may  be  read  or 
handed  to  the  teacher  to  look  over  out  of  class,  and  be  re- 
turned at  the  next  recitation. 

Some  of  the  sentences  assigned  should  be  correct,  some 
should  contain  an  error  to  be  corrected,  and  some  should  have 
introduced  into  them  some  error,  easily  detected,  to  hide,  as 
it  were,  some  other  error  not  so  easily  observed.  The  teacher, 
of  course,  should  inform  the  class  that  some  of  the  sentences 
are  correct,  some  contain  one  error,  some  two  errors,  etc.  It 
will  be  well  to  introduce  all  kinds  of  linguistic  errors  in  these 
exercises.  Thus  the  sentences  presented  may  contain  errors 
in  spelling,  in  the  use  of  capitals,  in  punctuation,  in  the  use  of 
words,  etc. 

Exercises  in  false  syntax  are  usually  found  in  the  text-book, 
and  may  be  studied  by  the  pupil  before  coming  to  the  recita- 
tion. The  teacher  may  also  prepare  a  list  of  such  incorrect 
sentences  as  seem  to  him  likely  to  be  used,  and  also  of  such 
as  he  has  met  with  in  his  reading  or  has  heard  in  the  vicinity 
of  the  school.     He  should  encourage  his  pupils  to  prepare  a 


TEACHING   ENGLISH   GRAMMAR.  285 

list  of  incorrect  sentences  which  they  may  hear  used,  and  also 
to  examine  the  books  they  are  reading  to  see  whether  they  can 
detect  any  errors  in  grammar.  Such  an  exercise  will  make 
their  grammatical  sense  very  susceptible  and  accurate,  and 
lead  to  great  care  in  their  own  use  of  language. 

In  conclusion,  we  remark  that,  with  the  more  advanced 
classes  in  parsing  and  analysis,  we  should  not  restrict  our- 
selves to  the  mere  technicalities  of  grammar,  but  should 
extend  the  exercise  so  as  to  cover  the  whole  subject  of  lan- 
guage. We  ma}'  call  attention  to  the  meaning  of  words,  to 
the  peculiarities  of  their  use,  to  the  etymology  of  prominent 
terms,  to  idiomatic  constructions,  to  the  allusions  of  history 
and  mythology,  to  the  use  of  capitals,  punctuation  marks,  etc. 
We  should  combine  the  elements  of  rhetorical  parsing  with 
grammatical  parsing,  and  so  conduct  the  exercise  as  to  give 
the  pupil  a  knowledge  of  the  correct  use  of  language  in  its 
widest  sense,  and  cultivate  a  critical  and  appreciative  literary 
taste.  In  this  way  an  exercise  in  parsing  and  analysis  ma} 
be  made  one  of  the  most  interesting  and  valuable  exercises  in 
the  entire  course  of  study. 


CHAPTER   IX. 

TEACHING   COMPOSITION'. 

COMPOSITION  is  the  art  of  expressing  our  ideas  and 
tliouglats  in  words.  It  is  the  art  of  telling  what  we  know, 
or  of  embodying  our  knowledge  in  language.  This  knowledare 
may  consist  of  facts  which  we  have  observed,  heard,  or  read; 
or  of  thoughts  which  we  may  have  acquired  by  conversation 
and  reading,  or  developed  by  thinking. 

Importance. — Composition  is  one  of  the  most  Important 
branches  taught  in  our  schools.  It  does  more  to  prepare  a 
pupil  for  success  in  many  departments  of  life  than  almost  anj^ 
other  branch.  It  also  attbrds  valuable  culture  to  the  mind, 
for  it  reijuires  closeness  of  observation,  fullness  and  readiness 
of  memor}',  and  the  power  of  original  thought  and  generaliza- 
tion. It  is  valuable  for  its  own  sake;  the  art  of  correct  and 
elegant  expression  is  an  accomplishment  to  be  highly  prized. 
It  also  cultivates  a  literary  taste  that  enables  one  to  appreci- 
ate the  works  of  literature,  and  thus  becomes  a  source  of  the 
most  refined  and  exquisite  pleasure.  • 

Composition  is  also,  when  properly  taught,  one  of  the  most 
interesting  and  delightful  of  the  common  school  branches. 
The  popular  dread  of  composition  writing  is  due  to  the  fact 
that  it  has  been  so  poorly  taught  in  our  schools.  There  can 
be  no  intrinsic  repulsiveness  in  writing  compositions.  Chil- 
dren love  to  talk,  the}'  delight  in  expressing  their  ideas  and 
feelings;  and  if  they  are  taught  to  understand  that  composi- 
tion is  merely  writing  what  they  know  and  think,  as  they 
would  talk  it,  pupils  would  take  delight  in  writing  composi- 
tions, and  long  for  "  composition  day  "  more  than  they  now 
dread  it 

(286) 


TEACHING   COMPOSITION.  287 

Errors  in  Tettchiuff. — The  errors  in  teaching  composition 
are  numerous.  Our  methods  give  i)upils  a  wrong  idea  of  the 
nature  of  composition  writing.  Many  pupils  seem  to  have  the 
idea  tliat  writing  a  composition  is  tr3'ingto  express  what  they 
do  not  know,  or  the  stringing  of  words  together  after  some 
mechanical  model,  instead  of  merely  writing  simply  and  natu- 
rally what  the}'  know  or  think  about  something.  Pupils  have 
been  required  to  write  compositions  without  any  instruction 
or  })reparation  for  the  exercise,  and  allowed  to  write  blindly 
without  any  assistance.  The  subjects  assigned  are  often  un- 
puited  to  pupils,  being  too  abstract  and  difficult.  Teachers 
have  made  the  subject  too  formal,  and  thus  taken  all  the  life, 
freshness,  and  zest  out  of  it. 

Such  teaching  has  given  the  pupils  of  our  public  schools  a 
dread  of  composition-writing.  They  regard  it  as  the  "  bug- 
bear "  of  the  school-room  ;  and  think  of  "  composition  day  " 
wiLh  a  shudder.  They  perform  the  allotted  task  without  any 
interest,  merely  because  the}'  are  compelled  to  do  so.  They 
l)ut  it  oif  to  the  last  moment,  and  slip  out  of  it  whenever  they 
can.  They  copy  their  compositions  out  of  books,  or  get  some 
older  pupils  to  write  for  them.  They  acquire  stilted  and  arti- 
ficial forms  of  expressing  themselves,  instead  of  writing  in 
that  natural  and  interesting  stj'le  in  which  the}'  converse. 

There  is  great  need  of  reform  m  this  respect,  and  this  need 
seems  to  be  widely  felt.  It  is  an  oft-repeated  question.  How 
shall  we  improve  our  methodsof  teaching  composition  ?  Our 
educational  periodicals  are  crowded  with  criticisms  of  the  old 
methods  and  suggestions  for  improvement.  Authors  are 
turning  their  attention  to  the  subject,  and  text-books  are 
multiplying  upon  it.  Our  grammars  are  growing  more  prac- 
tical, and  text-books  on  Language  Lessons,  designed  to  teach 
expression,  are  becoming  abundant. 

Division  of  the  Subject. — In  the  discussion  of  the  snbject, 
we  shall  speak  first  of  the  Preparation  for  Composition  Writ- 
ing, and  secondly,  of  the  Methods  of  Teaching  Composition 


'28S  METHODS   OF   TEACHING. 

The  Preparation  for  Composition  will  include  a  statement  of 
those  conditions  and  that  culture  which  prepare  a  pupil  for 
writing.  Instruction  in  Composition  will  embrace  first  that 
primary  instruction  which  is  designed  to  prepare  a  young 
pupil  to  express  himself  in  writing  with  correctness  and  free- 
dom. These  exercises  are  now  popularly  known  as  Language 
Lessons.  Under  the  second  head  we  shall  present  some 
formal  directions  for  Writing  a  Composition. 

I.  Preparation  for  Composition  Writing. 

Conditiojis. — The  fundamental  conditions  of  composition 
are, — first,  something  to  say,  and  secondl}-,  how  to  saj'  it.  In 
other  words,  composition-writing  includes  the  matte?'  and  the 
expression.  The  matter  consists,  in  a  general  waj',  of  ideas 
and  thoughts.  For  the  expression  of  these,  we  need  a  large 
and  choice  vocabulary  of  words^  and  a  finished  and  accurate 
style  of  expression. 

The  first  requirement  in  writing  composition  is,  that  there 
shall  be  something  to  say  ;  when  there  is  nothing  in  the  mind, 
nothing  can  come  out  of  it.  Here  is  the  mistake  of  many 
teachers,  who  expect  children  to  express  ideas  on  a  subject 
when  they  have  no  ideas  to  express.  Ideas,  thoughts,  knowl- 
edge in  the  mind,  it  should  be  remembered,  are  the  necessary 
antecedents  to  expression.  In  the  second  place,  there  must 
be  something  with  which  to  express  what  we  know.  Our 
knowledge  must  flow  out  in  the  form  of  words ;  and  we  must 
be  familiar  with  individual  words  and  know  how  to  use  them. 
The  third  condition  is  that  we  shall  acquire  a  clear  and  cor- 
rect method  of  expressing  our  thoughts;  and  cultivate,  so  far 
as  possible,  those  graces  of  style  which  give  beauty  and  finish 
to  expression.  Let  us  inquire  how  each  one  of  these  condi- 
tions is  to  be  attained. 

Sources  of  Material. — The  materials  of  composition,  as 
already  stated,  are  ideas,  facts,  thoughts,  sentiments,  etc. 
There  are  several  sources  of  these  materials.     The  principal 


TEACHIXQ   COMPOSITION.  289 

sources  of  our  ideas  and  thoughts  ai'e  Observation,  Reading, 
Judgment,  Imagination,  and  Reflection. 

Observation. — Man}'  of  our  ideas  come  from  the  observa- 
tion of  the  ol)jects  of  the  material  world.  The  facts  which  we 
express  are  drawn  largel}'  from  our  experience  of  things  and 
persons.  Nearly  all  the  great  writers  have  been  close  ob- 
servei's  of  nature  and  human  nature.  Homer  was  in  deep 
sympathy  with  the  material  world,  and  drew  some  of  his  finest 
figures  from  his  observation.  Shakespeare  was  a  devoted 
lover  of  nature,  and  gives  us  hundreds  of  pictures  like  "  The 
morn  in  russet  mantle  clad,  walks  o'er  the  dew  of  yon  high 
eastern  hill,"  showing  how  close  and  accurate  was  his  obser- 
vation. Dickens  drew  manj'  of  his  characters  from  actual 
persons  whom  he  knew,  and  whose  peculiarities  he  had  care- 
fully studied. 

Pupils  should,  therefore,  be  taught  to  observe  closely  and 
accurately.  Objects  should  be  presented  to  them  to  examine 
and  describe.  They  should  be  required  not  only  to  observe 
the  principal  features,  but  also  to  notice  the  minutise  of  things. 
Observation  should  be  analytic,  descending  to  the  minor  and 
less  obtrusive  parts  of  objects.  Trained  in  this  way,  a  pupil 
will  acquire  accurate  ideas  of  things,  and  be  able  to  point 
them  out  and  to  describe  what  he  has  seen  with  ease  and 
accuracy. 

Reading. — We  can  also  obtain  ideas  and  thoughts  b}''  Read- 
ing. In  books  we  find  facts,  ideas,  sentiments,  opinions, 
figures  of  rhetoric,  etc.,  which  remain  in  our  memor}^  and  may 
be  used  i?\  their  original  form,  or  become  types  for  creations 
of  our  own.  In  books  are  embalmed  the  choicest  productions 
of  the  master  minds  ;  and  they  enrich  the  mind  of  the  reader, 
and  give  wisdom  to  his  thought,  and  grace  to  his  utterances. 
Young  persons  should  cull  in  their  reading  the  finest  pas- 
sages, and  write  them  down  and  commit  them,  The\'  should 
also  take  note  of  the  interesting  and  important  facts  in  their 
bearing"  on  the  subject,  and  fix  them  in  the  memory.  An 
13 


290  METHODS    OF   TEACHING. 

effort  should  be  made  to  become  familiar  w.th  the  opinions 
and  noble  sentiments  of  the  great  thinkers,  for  in  this  way 
thoucht  will  be  enriched  and  expression  beautified. 

Judgment. — Pupils  should  be  taught  to  exercise  the  Judg- 
ment as  well  as  the  eyes  and  ears.  They  should  be  taught  to 
compare  things,  to  see  their  relations,  and  to  draw  inferences 
from  them.  They  should  be  required  not  only  to  see,  but  to 
think  about  what  they  see  ;  and  to  form  opinions  concerning 
it.  It  is  this  observing  with  the  jutlgment  that  makes  the 
philosopher.  By  it  Copernicus  attained  to  the  true  idea  of 
the  i)lanetary  system,  and  Newton  reached  the  great  law  of 
universal  gravitation. 

Imagination. — Pupils  should  be  taught  also  to  exercise  the 
Imagination.  Every  form  of  nature  not  only  embodies  an  idea, 
but  may  be  perceived  as  the  symbol  of  an  idea.  The  things 
of  the  material  world  are  typical  of  the  things  of  the  spiritual 
world  ;  they  are  often  the  symbols  of  ideas  and  sentiments  and 
feeliniis.  Here  is  the  source  of  personifications,  similes,  met- 
ai)hors,  etc.  The  flower  looks  up  into  our  eyes,  the  streamlet 
bathes  the  brows  of  the  drooping  violets,  the  stars  are  the 
forget-me-nots  of  the  angels,  etc.  It  is  the  office  of  the  Imag- 
ination to  catch  these  analogies,  to  transmute  the  material 
thing  into  the  immaterial  thought,  and  "give  to  airy  nothing  a 
local  habitation  and  a  name." 

The  Imagination  may  thus  be  taught  to  leap  from  the  visi- 
ble form  to  the  invisible  image.  Things  may  become  the 
ladder  by  which  it  rises  to  the  sphere  of  beautiful  and  poetic 
thoughts.  Thus,  Shakespeare  gives  us  the  figure  "  How  sweet 
the  moonlight  sleeps  upon  this  bank;"  Alexander  Smith  says, 
"  The  princely  morning  walks  o'er  diamond  dews ;"  and  Long- 
fellow gives  us  the  picture  of  a  "  silver  brook"  which  "bab- 
bling low  amid  the  tangled  woods,  slips  down  through  moss- 
gnnvu  stones  with  endless  laughter."  The  attention  of  the 
learner  should  be  called  to  these  and  similar  creations,  and  he 
should  be  encouraged  to  create  images  of  his  own. 


TEACHING   COMPOSITION.  291 

Reflection. — Much  of  the  material  of  compositions  comes 
from  Thinking.  We  must  therefore  learn  to  think  in  order 
to  learu  to  write.  It  is  not  enough  to  acquire  the  thoughts  of 
others  ;  we  must  learn  to  evolve  thoughts  for  ourselves.  We 
must  cultivate  a  reflective  and  creative  cast  of  mind  that  seeks 
for  the  idea  l^'ing  back  of  the  fact,  that  searches  for  the  cause 
of  the  phenomena,  and  is  ever  inquiring  what  these  facts  prove, 
or  what  principle  they  illustrate  or  establish.  We  should  en- 
deavor to  originate  new  forms  of  expression,  new  figures  of 
rhetoric,  and  to  form  ideas  and  opinions  of  our  own  on  many 
subjects. 

Sources  of  Words. — The  second  condition  of  becoming  a 
good  writer  is  the  acquisition  of  words.  In  order  to  write,  we 
must  not  only  have  ideas  and  thouglits,  but  we  must  have  lan- 
guage in  which  to  express  them.  The  thought  is  to  be  incar- 
nated in  speech.  Ideas  and  thoughts  existing  in  the  mind, 
intangible  and  invisible,  are  to  be  transmuted  into  audible  or 
visible  forms.  Nature,  as  it  were,  goes  into  the  mind  through 
the  senses,  and  reappears  in  the  form  of  language.  Form  and 
color  and  tone  in  the  natural  world,  give  form  and  color  and 
tone  to  expression.  The  freshness  of  spring,  the  brightness 
of  summer,  the  rich  tints  of  autumn,  and  the  silver  habit  of 
winter,  all  give  freshness  and  beauty  and  glory  to  the  litera- 
ture and  language  of  a  people.  These  words  may  be  acquired 
in  several  ways. 

Instinct. — Words  are  derived  partly  by  an  instinctive  habit. 
We  pick  them  up  in  conversation  without  any  conscious 
etTort.  A  child  will  often  be  heard  to  use  words  which  it  but 
a  short  time  before  heard  some  one  else  make  use  of.  Chil- 
dren seem  to  have  an  instinct  for  language,  and  new  words 
cling  to  their  memory  like  burrs  to  the  garments.  A  child  of 
four  years  of  age  ma}--  be  able  to  speak  three  or  four  different 
languages  if  it  has  had  an  opportunity  to  hear  them  spoken. 
It  is,  therefore,  of  great  advantage  to  a  child  to  hear  a  large 
and  expressive  vocabularj'  used  in  the  household. 


292  METHODS   OF  TEACHING. 

Conscious  Effort. — "Words  should  also  be  consciously 
acquired.  Tliere  should  be  a  special  effort  made  to  enrich  the 
vocabulary.  We  should  notice  the  words  in  our  reading,  and 
make  a  list  of  new  words,  or  of  those  which  we  may  think  do 
Hot  belong  to  our  practical  vocabulary.  Such  a  list  may  often 
be  reviewed  until  the  mind  becomes  familiar  with  it.  We 
should  also  make  use  of  these  words  in  our  conversation  and  in 
writing.  It  is  surprising  how  rapidl}'  we  would  improve  in 
expression  by  the  adoption  of  this  method.  Our  vocabulary, 
which  is  often  small,  smaller  than  we  think,  will  l)ecome  en- 
larged; and  we  will  learn  to  speak  and  write  with  a  copious, 
rich,  and  elegant  expression. 

The  Dictionary. — The  pupil  sliould  form  the  habit  of  study- 
ingr  the  Dictionarv.  The  dictionary  has  sometimes  been  used 
as  a  text-book  in  schools,  but  this  is  not  recommended;  it 
should,  however,  be  a  student's  constant  companion.  It  should 
lie  on  every  student's  table,  and  be  frequently  consulted. 
This  has  been  the  habit  of  some  of  the  most  accomplished 
scholars  and  writers.  Charles  Sumner  was  a  most  assiduous 
student  of  the  dictionary.  He  had  several  copies  in  his  library 
in  constant  use,  and  usuallj^  carried  a  pocket  edition  with  him; 
and  they  were  found,  after  his  death,  to  be  the  most  thumbed 
of  an}^  of  his  books.  Lord  Chatham  went  twice  through  the 
largest  English  dictionary,  studying  the  meaning  of  each 
word  and  its  various  uses. 

General  Reading. — An  extensive  course  of  general  reading 
is  valuable  in  acquiring  a  large  and  choice  vocabulary  of 
words.  Such  reading  should  be  largely  confined  to  our  best 
authors,  those  who  use  words  with  correctness  and  artistic 
skill.  The  finished  and  thoughtful  writer  often  puts  a  mean- 
ing in  a  word  which  we  never  noticed  before,  and  thus  stamps 
it  upon  our  memory.  It  is  only  in  this  way  that  we  can  ac- 
quire that  nice  and  delicate  sense  in  the  use  of  words  which 
distinguishes  the  refined  and  scholarly  writer. 

Ancient  Languages. — The  study  of  the  ancient  languages 


TEACHING    COMPOSITION.  293 

IS  especially  valuable  in  this  respect.  It  was  formerly  thought 
that  a  knowledge  of  Latin  and  Greek  was  necessary  in  order 
to  understand  the  English  language  ;  but  this  claim  is  now 
seldom  made.  The  great  value  of  their  study  consists  in  the 
constant  use  of  English  words  in  the  translations,  and  in  the 
comparison  and  weighing  of  the  sense  of  the  various  words 
given  in  the  definitions  to  see  which  will  express  the  meaning 
of  the  text  the  most  accuratel3\  If  the  student  should  forget 
every  word  of  Latin  and  Greek  the  year  after  he  leaves  college, 
the  linguistic  culture  he  has  received  is  a  permanent  posses- 
sion, and  will  enrich  his  expression. 

Small  Words. — In  the  choice  of  words,  young  pupils  should 
be  careful  not  to  select  merely  the  large  words.  The  large 
words  attract  the  attention  and  are  the  most  liable  to  be  re- 
membered. It  is  the  little  words,  however,  that  are  the  most 
expressive,  and  are  the  most  artistic  in  use.  The  good  old 
Anglo-Saxon  basis  of  our  speech  contains  a  richer  and  more 
expressive  meaning  than  the  larger  Latin  and  Greek  deriva 
tives.  Our  best  writers  delight  in  the  skillful  use  of  the  small 
words  ;  and  this  is  an  especial  characteristic  of  Shakespeare 
and  our  English  Bible. 

This  caution  is  the  more  necessary,  as  young  persons  have 
an  idea  that  large  words  indicate  learning  and  profund- 
ity of  thought.  Goethe  refers  to  this  when  he  makes  Mephis- 
topheles  say  to  Faust,  "  For  that  which  will  not  go  into  the 
head,  a  pompous  word  will  stand  j'ou  in  its  stead."  This  is 
quite  a  general  opinion  among  the  uncultured.  The  man  who 
came  to  his  minister,  frightened  at  a  strange  appearance  of 
the  sun,  was  entirely  satisfied  when  he  was  told  that  it  was 
"only  a  phantasmagoria."  Hazlitt,  referring  to  the  use  of 
large  words,  says,  "I  hate  anything  that  occupies  more  space 
than  it  is  worth;  I  hate  to  see  a  load  of  empty  bandboxes  go 
down  the  street,  and  I  hate  to  see  a  parcel  of  big  words  with- 
out anj'thing  in  them."  Leigh  Hunt  gave  a  fitting  reply  to  a 
lady   who   asked   the   question,    "Will   3^011  venture   on    an 


294  METHODS    OF   TEACHING. 

orange?"  by  his  answer,  "No,  thank  you,  I  fear  I  should  fall 
off."  Let  the  pupil,  therefore,  not  select  the  large  words, 
but  learn  to  use  the  little  words,  the  language  of  the  heart  and 
home,  with  skill  and  artistic  effect. 

Style  of  Ex^ivession. — We  not  only  need  ideas  and 
thoughts,  and  a  rich  vocabulary  in  which  to  express  them,  but 
we  need  also  to  know  how  to  put  these  words  together  to 
produce  the  best  results.  We  need  to  acquire  a  good  st3le 
of  expression.  We  need  to  acquire  that  ease  and  elegance 
of  expression  and  that  artistic  skill  in  the  use  of  language, 
which  distinguishes  the  cultivated  writer.  In  order  to  aid 
the  pupil  in  this,  several  suggestions  are  made. 

Read  Extensively. — First,  we  remark  that  pupils  should 
read  extensively.  Reading  not  only  gives  words,  but  it  gives 
facility  in  the  use  of  words  and  the  expression  of  ideas. 
Pupils  who  have  read  most  are  usually-  the  best  writers.  We 
often  find  in  school  those  who  are  deficient  in  the  more  diffi- 
cult studies,  yet  who  write  excellent  compositions  ;  and  upon 
inquiiy,  learn  that  they  have  read  a  great  deal,  perhaps  merely 
novels.  The  best  scholars  in  the  school  branches  are  often 
very  poor  writers,  because  they  have  done  but  little  reading. 
By  reading,  we  become  familiar  with  the  style  of  an  author, 
and  form  a  stjle  of  our  own.  Many  distinguished  men  have 
formed  their  style  b^^  reading  a  few  books  very  thoroughly, 
Lincoln  received  his  language  culture  ver}^  largely  from  read- 
ing the  Pilgj'im^s  Progress.  Kossuth's  masterly  knowledge 
of  English  was  acquired  by  the  study  of  Shakespeare  and  the 
English  Bible.  The  unique  and  expressive  language  of  un- 
cultured men,  derived  almost  entirely  from  reading  the  Bible, 
has  often  been  a  surpi-ise  to  us  and  demonstrated  the  utility 
of  reading  in  acquiring  a  style  of  expression. 

Copy  Productions. — Pupils  should  be  required  to  coyy  lite- 
rary productions.  Copying  an  author  will  make  a  deeper 
impression  than  even  a  careful  reading  of  one.  Sight  strikes 
deeper   than    sound ;  to   execute   form   stamps    it   upon  the 


TEACHING    COMPOSITION.  295 

nemory  like  a  die.  To  go  over  a  production,  word  by  word 
md  sentence  by  sentence,  writing  it  out,  will  impress  the 
style  of  the  author  deeply  upon  the  literary  sense.  I  would 
therefore  require  pupils  to  "copy  compositions."  If  a  para- 
gra[)h  could  be  written  every  day  on  the  slate  or  on  paper,  it 
would  greatly  aid  the  literary  growth  of  the  pupil.  Many 
eminent  writers  have  practiced  copying  the  productions  of  the 
masters  of  literature.  Demosthenes  copied  the  history  of 
Thucydides  eight  times,  in  order  to  acquire  his  clear,  concise, 
and  elegant  st3'le. 

Commit  Extendvell|.—V\\^^\\^  should  be  required  to  commit 
extensively,  both  prose  and  poetry.  Committing  will  make  a 
deeper  impression  than  either  reading  or  copying.  It  will 
tend  to  fix  the  words  and  deepen  the  channels  of  thought  and 
expression.  It  will,  a'^  it  were,  give  one  literary  moulds  in 
which  to  run  his  own  thoughts,  or  dig  out  literary  channels  in 
which  our  thoughts  and  sentiments  may  flow.  This  has  been 
the  practice  of  all  who  have  obtained  excellence  in  the  use  of 
language.  Burke  and  Pitt  cultivated  their  wonderful  powers 
of  oratory  by  committing  the  orations  of  Demosthenes.  Fox 
committed  the  book  of  Job,  and  drew  from  it  his  grandeur 
and  force  of  expression.  Lord  Chatham  read  and  re-read  the 
sermons  of  Dr.  Barrow  until  he  knew  many  of  them  by  heart. 

Declamation.— l^ha  old  practice  of  "  declaiming  pieces"  was 
of  very  great  value  to  students  in  the  culture  of  literary 
power.  It  gave  them  models  of  style  and  stimulated  expres- 
sion. Indeed,  it  often  did  more  to  give  a  command  of  English 
than  the  whole  college  course.  We  have  noticed  the  style  of 
young  men  after  their  graduation  at  college,  and  could,  in 
several  instances,  trace  it  back  to  the  culture  derived  from 
their  declamation  pieces. 

All  this  preparation  for  writing  requires  time  and  patience. 
It  cannot  be  acquired  in  a  few  months  or  a  year,  but  is  a 
matter  of  gradual  development.  Literary  skill  is  the  result 
of  literary  growth.      A    student  can  master  a  text-book  in 


296  METHODS   OF   TEACHING. 

geometiy  or  algebra  in  a  few  months ;  but  literary  culture  is 
the  work  of  a  life-time.  It  is  an  organic  product,  like  the 
development  of  a  tree.  The  exercises  should  be  continued 
day  by  day,  and  the  result  will  crown  the  work.  We  shall 
now  proceed  to  the  second  division  of  the  subject, — The 
Methods  of  Teaching  Composition.  We  shall  divide  the  sub- 
ject into  two  parts ;  Language  Lessons  and  Composition 
Writing. 

II.  Language  Lessons. 

The  preparatory  exercises  required  for  young  pupils  in 
learning  to  understand  and  use  the  English  language  with 
skill,  have,  by  common  consent,  received  the  name  of  Lan- 
guage Lessons.  By  Language  Lessons  we  mean  such  element- 
ary training  in  the  use  of  language  as  shall  enable  a  pupil  to 
understand  and  appreciate  language,  and  to  use  it  with  cor- 
rectness, ease,  and  elegance. 

Niiture  ami  IiiiportttHce. — Of  the  importance  of  such  les- 
sons there  can  be  no  doubt.  The  primary  object  of  education 
in  language  is  to  learn  to  use  language.  In  order  to  leara  the 
correct  use  of  language,  we  must  notice  and  use  language. 
The  use  of  language  is  an  art ;  and  we  learn  the  art  by  imita- 
tion and  practice.  In  order  to  learn  to  talk  well,  we  must 
hear  good  talking  and  practice  talking.  In  order  to  learn 
to  write  well,  we  must  notice  good  composition  and  practice 
writing  ourselves. 

A  system  of  Language  Lessons  conforms  to  nature's 
method  of  teaching  language.  The  little  child,  prattling  in 
its  mother's  arms,  is  engaged  in  its  first  lessons  in  composi- 
tion. The  simple  name,  the  quality  and  action  word,  the 
short  sentence,  etc.,  all  come  in  the  natural  growth  of  the 
power  of  expression.  In  teaching,  we  must  observe  nature's 
method  and  follow  her  golden  rules.  A  correct  system  of 
language  lessons  is  founded  upon  the  way  in  which  a  little 
child  naturally  learns  oral  and  written  language. 


TEACHING    COMPOSITION.  297 

A  system  of  language  lessons  will  also  teach  a  child  to 
acquire  and  produce  knowledge  as  well  as  to  express  it.  It 
cultivates  the  habit  of  observation  and  comparison  ;  and  thus 
leads  a  child  to  think  as  well  as  to  express  thought.  Subjects 
should  be  assigned  that  require  attentive  examination,  that 
call  the  judgment  into  activity,  and  that  lead  the  pupil  to 
investigate  and  discover  facts,  and  thus  gain  knowledge  for 
himself.  The  pupil  will  also  be  taught  to  classify  the  knowl- 
edge obtained  from  reading,  to  sift  its  true  meaning,  and  to 
express  in  his  own  words  the  thoughts  of  the  writer  he  has 
studied. 

The  fundamental  principle  of  these  lessons  is  that  pupils 
are  to  be  taught  the  practical  use  of  language  by  the  use 
of  language  rather  than  by  a  study  of  the  principles  of  lau- 
o-uaffe.  There  should  be  an  imitation  of  models,  and  a  free 
and  spontaneous  expression  of  ideas,  without  any  thought  of 
the  grammatical  rules  or  principles  involved.  For  example, 
the  pupil  should  express  himself  in  sentences  without  any 
thought  of  the  subject  and  predicate  of  a  sentence,  and  use 
the  ditferent  parts  of  speech  without  any  knowledge  of  them 
as  parts  of  speech.  He  should  use  nouns  and  verbs  without 
knowing  that  they  are  nouns  and  verbs;  form  plurals  without 
any  rules  for  numbers;  use  cases,  modes,  tenses,  etc.,  without 
knowing  that  there  are  such  things  as  cases,  modes,  tenses,  etc. 

The  system  of  language  lessons  aims  to  teach  the  use  of 
language  by  imitation  and  practice  rather  than  by  the  study 
of  rules  and  definitions.  The  object  is  to  give  children  a 
knowledge  of  the  uses  of  words  and  the  power  to  express  their 
ideas,  without  clogging  their  memories  with  grammatical 
terms  which  are  to  them  often  only  abstract  sounds  without 
any  content  of  meaning.  The  pupils  are  brought  into  contact 
with  living  language,  and  not  the  dead  dry  skeleton  of  gram- 
matical definitions  and  rules ;  and  this  living  spirit  becomes 
engrafted  on  their  own  language  until  it  becomes  a  part  of 
their  nature. 
13* 


298  METHODS   OF   TEACHING. 

According  to  this  principle,  a  knowledge  of  language  should 
precede  a  knowledge  of  grammar.  This  is  the  historical  order 
of  development.  The  ancients  knew  language  and  could  use 
it  in  literature,  but  they  had  very  little  knowledge  of 
grammar.  Homer  sang  in  immortal  verse,  and  probably 
hardl}^  knew  a  noun  from  a  verb.  The  Iliad  embodied  the 
rules  of  grammar,  without  the  author  being  conscious  of 
them ;  the  rules  of  grammar  were  derived  from  the  study  of 
the  Iliad.  This  is  also  the  natural  order, — practice  precedes 
theory,  the  art  comes  before  the  science, — and  should  be  fol- 
lowed in  the  early  lessons  on  language. 

Another  principle  is  that  language  lessons  should  lead  to 
and  be  the  basis  of  grammatical  instruction.  Most  of  our 
tert-books  on  language  lessons  invert  this  order  by  basing  the 
lessons  in  language  on  grammar.  This  is  a  ver^-  gi-eat 
mistake,  and  vitiates  the  whole  course  of  instruction.  The 
largua2:e  lessons  should  prepare  for  and  lead  up  to  grammar. 
Grammar  may  then  return  the  favor  and  aid  in  the  correct  use 
of  language.  Thus  art  gives  birth  to  science,  and  science 
reciprocates  the  faror  and  gives  perfection  to  art.  The  study 
of  grammar,  therefore,  should  not  be  begun  until  such  a 
course  in  language  lessons,  as  is  suggested,  has  been  completed. 

Such  lessons  should  be  begun  as  soon  as  the  child  can  write. 
Before  this  it  should  be  required  to  commit  and  recite  little 
poems  and  pieces  of  prose.  If  it  can  hear  good  models  of 
conversation,  it  will  be  of  very  great  advantage  in  the  culture 
of  con-ect  expression. 

Course  of  Lessons We  shall  now  present  an  outline  for  a 

course  of  Language  Lessons  suitable  for  beginners.  This  is 
a  mere  outline  and  is  to  be  filled  out  by  the  teacher  in  actual 
instruction. 

\.  Require  pupils  to  write  the  names  of  objects.  Write  the 
names  of  ten  objects  ;  the  names  of  objects  in  the  school- 
room; objects  in  the  house;  objects  they  can  see  h\  looking 
out  of  the  window;  objects  they  saw  in  coming  to  school,  etc. 


TEACHING   COMPOSITION.  299 

2.  Require  pupils  to  write  the  navies  of  actions.  Write 
tiie  actions  of  a  child  ;  of  a  bird  ;  of  a  dog  ;  of  a  cat ;  of  a  fish  ; 
of  a  horse  ;  of  a  cow;  of  a  cloud;  of  a  river,  etc. 

3.  Require  pupils  to  write  the  names  of  objects  with  the 
names  of  actions,  foi'miug  a  sentence.  Give  the  name  of  the 
object,  requiring  them  to  give  the  name  of  the  action  ;  also 
give  them  the  name  of  the  action,  requiring  them  to  give  the 
name  of  the  object. 

4.  Lead  pupils  to  an  idea  of  a  sentence,  as  asserting  some- 
thing of  something.  Lead  them  to  see  what  is  a  telling  or 
declarative  sentence,  an  asking  or  interrogative  sentence,  and 
a  commanding  or  imperative  sentence. 

5.  Teach  them  that  each  sentence  begins  with  a  capital  let- 
ter;  that  a  declarative  or  imperative  sentence  ends  with  a 
period,  and  an  interrogative  sentence  with  an  interrogation 
point.  Drill  them  in  writing  sentences  and  correcting  sen- 
tences which  violate  these  rules. 

G.  Have  them  write  sentences  introducing  adjectives^  ad- 
verbs, pronouns,  inte7Jections,  etc.  The  teacher  will  give  the 
word,  and  have  them  form  the  sentences.  Of  course  the 
pupils  are  not  to  know  an^'thing  about  these  words  as  parts 
of  speech. 

7.  Show  the  difference  between  particular  and  common 
names,  and  teach  the  use  of  capitals  for  particular  names. 
Teach  also  the  use  of  capitals  for  I  and  0.  Have  them  write 
exercises  involving  these  things,  and  correct  sentences  which 
violate  their  correct  use. 

8.  Give  two  words,  and  have  pupils  write  sentences  contain- 
ing them  both;  give  also  three  words  to  be  put  in  a  sentence, 
four  words,  etc.  The  pupils  ma}'  also  be  allowed  to  select 
the  words  which  the}'  are  to  unite  in  a  sentence. 

9.  Give  pupils  sentences,  with  words  omitted,  and  require 
them  to  insert  the  correct  words.  Such  sentences  can  be  dic- 
tated to  them,  the  missing  word  being  indicated  by  the  word 
"blank."     If  they  are  written  upon  the  board  for  them,  the 


300  METHODS   OF   TEACHING. 

missing  words  may  be  indicated  by  a  dash;  as,  "  I  saw  a 

building  a  in  a  tree."     The  teacher  should  select  and 

prepare   a   large   list   of  such   sentences    for  the  use  of  his 
pupils. 

10.  Have  the  pupils  look  at  an  object  and  describe  it.  Have 
them  descinbe  a  school-mate,  a  horse,  a  cow,  a  cat,  a  pig,  the 
school-house,  a  barn,  a  church,  etc.  A  very  interesting  exer- 
cise can  be  had  in  describing  one  another,  and  other  persons 
whom  they  know. 

11.  Have  pupils  look  at  a  picture,  and  tell  you  all  they  see 
in  it,  and  then  write  it  out  on  their  slates  or  on  paper.  Pic- 
tures can  be  found  in  the  primary  readers,  or  the  teacher  may 
bring  a  large  picture  to  school  for  the  pupils  to  look  at,  or 
pupils  may  bring  some  pictures  from  home. 

12.  Show  them  how  to  arrange  lines  of  poetry,  and  that  each 
line  begins  with  a  capital  letter.  Dictate  poetry  to  them,  and 
have  them  copy  it,  getting  the  lines  and  the  capitals  right. 
After  pupils  are  familiar  with  correct  formS;  they  may  be  allowed 
to  criticise  incorrect  forms  ;  as 

Mary  had  A  little  Lamb. 

its  Fleece  was  wiglit  As  snow  I 
and  Every  Where  that  marry  Went  ? 
The  Lamb  ;  was  shure  To  go  : 

13.  Have  pupils  talk  about  something,  and  then  write  down 
what  they  have  said  about  it.  Let  thom  learn  to  write  their 
talk.  Take  such  subjects  as  a  knife,  a  chair,  a  boat,  a  pin,  a 
needle,  a  cat,  etc.  Parts  of  the  body,  as  the  eyes,  the  nose, 
the  mouth,  the  tongue,  the  hands,  the  feet,  etc.,  are  easy  and 
interesting  subjects  for  children  to  talk  and  write  about. 

14.  Call  out  a  child's  knowledge  of  an  object  by  asking 
questions  about  it,  and  then  have  him  write  down  what  has 
been  said,  in  distinct  sentences.  Children  often  know  more 
about  an  object  than  they  can  think  of.  Questions  will  also 
lead  them  to  discover  new  things  about  the  object  that  they 
had  not  noticed  before,  and  teach  them  how  to  look  at  things 
and  gain  a  knowledge  of  them. 


TEACHING   COMPOSITION,  301 

15.  Talk  to  the  children  about  something,  have  them  repeat 
what  you  have  said  in  their  own  words,  and  then  write  it  out 
on  their  slates,  or  on  paper.  They  will  thus  see  that  writing 
a  composition  is  merely  telling  in  writing  what  they  know  and 
can  tell  in  talk. 

16.  Teach  them  the  use  of  the  hyphen,  as  connecting  com- 
pound words;  and  also  its  use  at  the  end  of  a  line,  in  con- 
necting one  syllable  with  the  S3'llable  beginning  the  next  line, 

17.  Teach  the  use  of  the  comma,  as  placed  after  the  name 
addressed;  as,  "John,  come  here;"  and  also  as  connecting 
three  words  of  a  series;  as,  ''  He  saw  a  boy,  a  girl,  and  a  dog." 

18.  Teach  the  use  of  the  period  after  abbreviations;  and 
make  pupils  familiar  with  the  common  abbreviations;  as,  Mr., 
Dr.,  Rev.,  Hon.,  Esq.  Drill  them  on  LL.D.,  so  that  they  will 
not  make  the  common  mistake,  "  L.  L.  D." 

19.  Teach  the  use  of  quotation  marks.     Show  that  the  in 
formal  quotation   is  set  otf  by  the   comma;   as,  Mary  said, 
"John,  come  here."     Show  also  that  a  divided  quotation  has 
two  commas;  as,  "To  be  good,"  says  some  one,  "is  to  bo 
happy." 

20.  Teach  also  the  use  of  the  colon  before  a  quotation  In- 
troduced formally  by  such  expressions  as  "the  following,'' 
"as  follows;"  as,  He  spoke  as  follows:  "Mr.  President,  .he 
gentleman  is  mistaken  in  his  facts,"  etc. 

21.  Teach  the  use  of  the  apostrophe  in  denoting  possession; 
as,  John's  book.  Also,  its  use  in  denoting  omission  of  letttrs; 
as.  Ne'er,  'T  is,  I  've,  etc. 

22.  Teach  the  use  of  the  exclamation  point  after  interiec- 
tions;  as,  Oh!  Alas  I  Pshaw!  Hurrah!  etc. 

23.  Let  the  teacher  read  a  narrative  and  ask  questions  on 
it,  and  then  have  the  pupils  reproduce  it  orally  and  in 
writing. 

24.  Write  sentences  on  the  board,  and  have  the  pupils  imi- 
fate  them  in  other  sentences.  Write  also  faulty  sentences  for 
them  to  correct.  Include  errors  upon  all  the  things  that  hav 
been  presented  in  these  Language  Lessons. 


302  METHODS   OF   TEACHING. 

25.  Give  related  simple  sentences,  and  require  pupils  to  unite 
them  into  compound  sentences.  Tlius,  "John  stood  up;" 
"John  spoke  to  his  father,"  changed  into  "John  stood  up  and 
spoke  to  his  father."  Let  them  also  decompose  compound 
sentences  into  simple  ones;  as  "John  and  Mary  went  home," 
changed  into  "John  Avent  home,"  and  "Mary  went  home." 

26.  Give  them  some  little  proverb,  and  have  them  write  out 
nn  explanation  of  it;  as,  "Little  children  should  be  seen  and 
not  heard;"  or,  "Birds  of  a  feather  flock  together;"  or,  "A 
rolling  stone  gathers  no  moss." 

27  Require  them  to  express  sentences  in  different  ways; 
as,  "  The  flowers  bloom  ver3'  sweetly  in  the  spring  of  the 
year,"  changed  to  "  In  the  spring  of  the  j'ear,  the  flowers 
bloom  verj'  sweetly." 

28.  Require  them  to  change  poetry  into  prose.  Write  a 
stanza  on  the  board,  and  have  them  express  the  same  thing  in 
prose;  as, 

"The  day  is  done,  and  the  darkness 
Falls  from  the  wings  of  Xight, 
As  a  feather  is  wafled  downward 
From  an  eagle  in  his  flight," 

Changed  to  "When  the  day  is  done,  the  darkness  falls 
arouud  us  as  gently  as  a  feather  which  falls  from  the  wing  of 
an  eagle  flving  above  us." 

29.  Exercise  them    on   misused  icords  and    incorrect  con 
structions;  as,  "I  expect   j'ou  had  a  good  time;"  "  Let  Mar}' 
and  I  go  out ;"  etc.     Make  a  full  list  of  the  incorrect  expres- 
sions in  common  use,  and  drill  the  pupils  in  their  correction. 

30.  Present  the  elements  of  Letter  Writing.  Teach  the  cor- 
rect form  of  the  Date,  Address,  Introduction,  Close,  Super- 
scription, their  punctuation,  and  the  correct  use  of  the  capitals 
which  occur  in  them.  The  teacher  who  does  not  understand 
the  subject  will  find  it  explained  in  Westlake's  How  to  Write 
Letters. 

31.  Require  pupils  to  write  letters  of  different  kinds;   as 


TEACHING    COMPOSITION.  303 

Business  Letters,  Notes  of  Invitation,  Notes  of  Acceptance, 
Excuses  for  Absence  from  Sciiool,  Receipts  for  Monej',  Due 
Bills,  Notes,  etc. 

32.  Have  them  -n-rite  a  letter  to  a  teacher,  to  a  friend,  to 
their  father,  to  their  mother,  to  a  school-mate,  etc.  They  will 
be  interested  in  writing  a  letter  to  a  dog,  or  a  horse,  or  a 
bird,  etc.,  imagining  that  the  animals  can  understand  thcni. 
Give  them  forms  of  letters  as  models  for  them  to  imitate. 

33.  Teach  them  a  few  of  the  simple  figures  of  rhetoric^  as 
the  Simile,  the  Metaphor,  Personification,  etc.;  and  require 
them  to  point  them  out  in  sentences  and  to  form  sentences 
containing  such  figures.  Have  them  change  metaphors  into 
similes,  and  similes  into  metaphors,  etc. 

8-4.  Have  them  write  little  newspai^er  paragraphs,  as  an 
account  of  a  fire,  of  a  party,  of  a  runawa}',  of  a  railroad  acci- 
dent, etc.  Bring  a  newspaper  into  school  and  read  such  items 
of  news  as  will  interest  them,  and  have  them  write  little  items 
in  imitation  of  those  in  the  paper. 

35.  During  all  this  time,  have  them  committing  and  reciting 
choice  selections  of  prose  and  poetry.  Do  not  allow  them  to 
repeat  these  mechanicallj'  without  understanding  their  mean- 
ing, but  ask  questions  to  lead  to  a  clear  idea  of  what  is  ex- 
pressed. This  will  cultivate  a  literary  taste,  which  lies  at  the 
basis  of  all  artistic  excellence  in  the  use  of  language. 

36.  Give  them  suitable  subjects  and  require  them  to  write 
little  compositions.  Let  the  subjects  be  simple,  and  of  per- 
sonal interest  to  them.  Indicate  the  method  of  treatment. 
Ask  questions  to  lead  them  to  what  should  be  written.  En- 
courage the  timid  and  diffident.  Suggest  how  to  state  facts, 
to  sa^-  bright  little  things,  to  express  ideas  and  sentiments,  etc. 
Lead  them  to  write  naturally,  expressing  what  they  think  ami 
feel.  Correct  kindly  and  gently,  and  sti'ive  to  make  them  love 
to  write  compositions. 

The  above  presents  a  ver^'  complete  outline  for  instruction 
in  Language  Lessons.     It  is,  howeA'er,  merel}-  an  outline,  and 


304  METHODS   OF   TEACHING. 

needs  to  be  filled  out  for  actual  use  in  the  school-room.  The 
teacher  should  take  this  outline  and  write  out  a  list  of  exam- 
ples or  exercises  under  each  head,  suitable  for  the  use  of  liis 
pupils.  No  text-book  in  the  hands  of  the  pupils  is  needed 
for  this  work,  if  the  teacher  is  properly  qualified  himself;  but 
each  teacher  will  find  it  of  advantage  to  write  out  a  little 
text-book  for  his  own  use  in  giving  instruction  in  language 
lessons.  To  aid  the  teacher  in  preparing  these  lessons,  we 
recommend  the  following  works  :  Hadley's  Lessons  on  Lan- 
guage, Llo3'd's  Literature  for  Little  Folks,  Bigsby's  Ele- 
ments of  the  English  Language,  and  Swinton's  Language 
Lessons. 

In  following  this  outline,  the  teacher  should  make  the  exer- 
cises very  full  and  complete.  Do  not  be  afraid  of  having  too 
much  under  each  head,  for  we  are  most  liable  to  err  by  not 
giving  practice  enough.  Let  the  motto  be  Make  haste  slowly. 
Give  variet}'  to  the  lessons,  and  pupils  may  be  kept  for  a  long 
time  on  each  exercise  suggested.  Keep  up  a  constant  review 
by  introducing  parts  of  the  previous  exercises  into  each  sub- 
sequent exercise. 

III.   The  Writing  of  a  Composition. 

We  shall  now  speak  of  teaching  a  pupil  to  write  a  composi- 
tion. The  previous  exercises  have  been  designed  for  begin- 
ners, and  are  mainly  imitative  in  their  character;  older  pupils 
should  depend  more  upon  themselves,  and  be  required  to  con- 
struct formal  compositions.  We  shall  speak  of  the  subject 
under  three  heads:  first,  the  Principles  to  guide  a  teacher  in 
the  instruction  ;  second,  the  Method  of  Writing  a  Composi- 
tion; and  third,  some  General  Suggestions  on  the  subject. 

I.  Principles  of  Composition  Writing. — In  teaching  pupils 
to  write  a  composition,  the  following  principles  should  be 
l>orne  prominentl}'  in  mind  : 

I.  Composition  is  to  he  regarded  as  the  expression  of  what 
a  child  actually  knows.     The  importance  of  this  principle  is 


TEACHING   COMPOSITION.  305 

enhanced  by  the  fact  that  it  has  been  very  generally  ignored 
by  teachers.  Many  pupils  go  to  work  at  their  compositions 
as  if  they  were  expected  to  tell  wliat  they  do  not  know.  The 
exercise  is  not  a  spontaneous  production  of  what  they  think, 
but  a  reaching  out  and  striving  after  that  which  they  have 
never  thought.  Tliis  will  account,  to  a  large  extent,  for  the 
general  distaste  for  composition  writing,  and  the  frequent  de- 
ception in  respect  to  their  authorship.  Teachers,  in  assigning 
subjects,  seem  to  have  been  oblivious  of  this  principle,  often 
giving  subjects  that  are  entirely  beyond  the  reach  of  the 
pupil's  experience  and  range  of  thought. 

2.  Pupils  should  begin  with  oral  compositions.  They  should 
be  required  to  talk  about  objects  before  writing  about  them. 
We  should  begin  by  having  pupils  talk  compositions  before 
they  write  compositions.  Subjects  can  be  assigned  the  same 
as  for  a  written  composition,  time  being  given  for  preparation 
or  not,  as  the  teacher  may  prefer.  Many  of  our  eminent 
editors  and  literary  men  talk  their  literaxy  productions,  and 
have  them  copied  by  an  amanuensis. 

3.  Pupils  should  be  led  to  see  that  writing  a  composition  is 
writing  their  talk.  This  is  the  key  to  composition  writing 
with  young  pupils.  This  principle  clearly  understood,  would 
be  like  a  revelation  to  many  a  pupil;  it  would  open  up  the 
way  and  remove  the  ditliculties  that  so  often  seem  to  rise  up 
mountain  high  before  them.  Many  persons  who  talk  well 
seem  to  grow  dumb  when  they  take  a  pen  in  hand;  what  they 
need  to  learn  is  to  write  their  talk. 

4.  Do  not  be  too  critical  at  first.  Severe  criticism  tends  to 
discourage  the  pupil,  and  create  a  distaste  for  the  subject. 
There  is  no  exercise  in  which  criticism  wounds  so  deeply  or 
discourages  so  soon  as  that  of  composition  writing.  Pupils 
need  encouragement  as  well  as  direction.  We  should  com- 
mend that  which  is  worthy  of  praise;  and,  in  a  kindly  manner, 
point  out  the  mistakes  and  suggest  where  improvements  can 
be  made. 


306  METHODS    OF   TEACHING. 

5,  3Iale  the  subject  intereating.  Cultivate  a  love  for  the 
expression  of  tlionght.  Be  an  inspiration  to  pupils  by  writing 
for  them  and  with  them.  Start  a  little  newspaper  in  the 
school,  and  have  them  contribute  to  its  columns.  Make  them 
feol  that  composition  writing  is  a  delightful  task;  the  most 
delightful  exercise  in  the  school.  They  will  thus  long  for 
"composition  day,"  instead  of  regarding  it  with  dread  or  in- 
ditference.  Remembering  these  principles,  the  teacher's  way 
in  teaching  composition  will  be  much  smoother  than  it  has 
been,  and  the  results  will  be  much  more  satisfactory.  Indeed, 
the  teacher  who  catches  the  spirit  of  these  principles,  ami  ap- 
plies them  properly,  can  make  the  pathway  all  bright  and 
fragrant  with  blossoms  of  interest,  both  for  himself  and  for 
his  pupils.  Some  of  the  author's  pleasantest  recollections  of 
school  life  are  associated  with  his  classes  in  composition. 

II.  WuiTiNG  A  Composition. — In  the  writing  of  a  eamiiosi- 
tion,  there  are  four  things  which  call  for  special  attention: 
1.  The  Subject;  2.  The  Matter;  3.  The  Analysis;  4.  The 
Amplijlcation. 

Each  of  these  is  modified  by  the  kind  of  composition  to  be 
written.  The  principal  kinds  of  composition  are  as  follows: 
1.  Description;  2.  Narratives;  3.  Essays;  4.  Discourses; 
5.  Fictions;  6.  Poems.  The  first  and  second  of  these  consist 
mainly  of  a  description  of  facts.  The  Essay  is  a  presentation 
of  thought  or  opinion  upon  some  subject:  in  a  large  sense  it 
may  include  Editorials,  Reviews,  and  Treatises.  Discourses 
are  productions  designed  to  be  read  or  delivered:  they  in- 
clude Lectures,  Sermons,  Addresses,  and  Orations.  Dis- 
courses usually  contain  both  thought  and  description. 

The  Subject. — The  Subject  of  a  composition  is  one  of  the 
most  important  parts  of  the  production.  To  select  or  invent 
a  good  subject  often  requires  more  thought  and  talent  than  to 
write  the  composition.  The  merit  of  a  literary  production 
often  depends  very  largely  on  the  selection  of  a  happy  and 
suggestive  topic. 


TEACHING    COMPOSITION".  307 

It  is  usualh'  best  for  the  teacher  to  assign  the  subject  to 
the  pupil.  He  can  better  adapt  it  to  the  taste  and  capacity  of 
the  pupil  than  the  pupil  can  himself.  Besides,  the  pupil  may 
not  only  select  au  inappropriate  subject,  but  will  often  spend 
more  time  in  making  the  selection  than  in  writing  upon  it. 
It  also  secures  more  variety  in  subjects  for  the  teacher  to 
select  them,  and  thus  gives  a  wider  culture  in  writing.  It 
also  removes,  to  a  great  extent,  the  temptation  to  plagiarize, 
as  the  pupils  cannot  so  readily  find  access  to  an  article  on  a 
given  topic  as  when  they  choose  the  topic.  At  times,  how- 
ever, pupils  should  be  required  to  select  and  invent  topics  for 
themselves,  as  it  is  an  excellent  exercise  for  their  ingenuity, 
and  tends  to  cultivate  independence  and  self-reliance  of 
thought.  Pupils  who  have  always  depended  on  the  teacher 
for  subjects,  become  very  helpless  when  placed  in  circum- 
stances where  the}'  must  make  their  own  selection. 

In  assigning  the  subject,  the  teacher  should  be  careful  to 
adapt  it  to  the  pupil.  Do  not  give  abstract  or  lofty  subjects 
about  which  the  pui)iU  have  no  ideas  or  knowledge.  What, 
for  instance,  does  a  little  child  know  about  Contentment,  or 
Immortality,  or  Government,  or  The  Sublimity  of  Thought, 
etc.?  Let  the  subject  be  one  that  appeals  to  the  pupil's  experi- 
ence. For  young  pupils,  subjects  like  going  to  school,  swim- 
ming, fishing,  skating,  coasting,  etc.,  would  be  appropriate; 
older  pupils  should  write  on  subjects  requiring  more  maturity 
of  thought  and  experience.  In  all  cases,  let  the  subject  be 
interesting  to  the  writer,  if  possible,  and  one  upon  which  he 
may  express  what  he  really  knows. 

Subjects  should  be  so  varied  as  to  give  practice  in  various 
st3-les  of  composition  Pupils  should  be  required  to  write 
descriptions. of  oljects.  pLices,  i)ersons,  natural  scenery-,  etc.; 
the}'  should  be  required  to  relate  incidents  of  their  observa- 
tion or  experience;  to  write  little  fictions,  allegories,  orations, 
dialogues,  etc. ;  and,  with  many  pupils,  an  exercise  in  writing 
poetr}'  will  also  be  of  real  value. 


808  METHODS   OF  TEACHING. 

The  subject  must  also  be  determined  by  the  kind  of  compo- 
sition to  be  written.  If  the  composition  is  designed  for  a 
public  audience,  it  should  be  of  popular  interest  and  suited  to 
the  intelligence  of  the  audience. 

The  subject  should  possess  unity,  and  be  clear  and  fresli. 
The  statement  of  it  should  be  simple,  not  too  figurative,  but 
happy  in  expression,  and,  if  possible,  striking.  The  manner 
of  stating  a  subject  often  gives  popularity  to  a  production.  A 
book  frequently  owes  a  large  share  of  its  popularity  to  its 
title.  The  title,  That  Husband  of  3Iine,  sold  many  more  coi)ies 
than  the  story  itself  merited,  and  became  a  model  for  the 
naming  of  a  score  of  other  works. 

The  Material. — When  the  subject  is  selected,  the  first 
thing  is  to  acquire  the  material  for  the  production.  There 
must  be  something  to  say  before  we  attempt  to  say  anything. 
We  cannot  draw  water  from  a  drj'  well.  This  getting  the 
material  is  called  Invention;  and  it  is  the  most  ditticult  part 
of  the  process  of  composing.  It  is  not  eas}'  to  sliow  how  it 
can  be  done.  Some  hold  that  it  is  not  a  thing  to  be  taught, 
that  "it  is  a  part  of  one's  native  endowment,"  an  original 
talent  and  not  a  power  to  be  acquired.  A  few  suggestions 
can  be  made,  however,  which  are  thought  to  be  valuable. 

The  material  of  a  composition  consists  of  facts  and  thoughts. 
Facts  embrace  such  things  as  have  been  observed  b}'  the 
writer  or  by  others.  The  thoughts  embrace  opinions,  senti- 
ments, figures  of  rhetoric,  etc.  This  material  may  be  obtained 
from  at  least  five  different  sources;  Observation,  Conversation, 
Reading,  Imagination,  and  Reflection.  These  are  treated 
quite  fully  under  Prepatration  for  Composition  Writing,  and 
need  not  be  discussed  here.  They  are  more  or  less  prominent 
in  supplying  the  material,  according  to  the  character  of  ohe 
subject  upon  which  one  is  writing. 

Observation. — If  the  subject  is  descriptive  or  narrative,  a 
writer  should  draw  first  from  his  own  observation.  That 
which  is  stamped  with  a  writer's  personality,  is  far  more  in- 


TEACHING   COMPOSITION.  809 

teresting  than  what  he  gives  at  second  hand.  Some  one 
happily  remarks,  "Do  not  go  to  Homer  for  a  sunrise  when 
you  can  see  one  every  morning."  In  the  second  place,  the 
writer  should  draw  from  the  experience  of  others,  which  may 
be  done  by  conversation  or  by  reading.  Much  can  be  picked 
up  in  conversation  that  will  be  fresh  and  interesting.  In  the 
use  of  books,  select  only  those  things  that  are  most  attractive, 
and  endeavor  to  express  these  facts  in  your  own  language. 
When  the  material  derived  fi-ora  these  several  sources  is 
abundant,  make  use  of  that  which  seems  to  possess  the  most 
novelty. 

Imagination. — Try  to  throw  the  light  of  fancy  around  this 
material.  The  plain  fact  is  not  of  so  much  interest  as  when  it  is 
made  to  glow  with  the  touch  of  imagination.  Let  the  fact 
awaken  an  image  in  the  mind,  if  possible ;  draw  from  it  a  simile 
or  a  metaphor ;  endue  it  with  the  life  of  a  personification,  etc. 
Many  writers,  like  Scott  and  Dickens,  weave  the  most  beautiful 
fancies  into  their  statements  of  facts  and  cast  a  charm  over  the 
descriptions  of  the  most  ftimiliar  objects. 

Reflection. — If  the  subject  is  reflective  in  its  character,  the  ma- 
terial will  consist  principally  of  thoughts  and  opinions.  These 
thoughts  and  opinions  are  attained  by  thinking,  by  reading,  and 
by  conversation.  A  writer  should  first  try  to  think  out  all  he  can 
for  himself.  And  here  the  question  arises,  how  shall  we  evolve  or 
create  thoughts  by  thinking?  No  rule  can  be  given,  but  a  few  sug- 
gestions will  be  ventured. 

First,  we  should  put  ourselves  in  a  reflective  mood ;  we 
should  fix  the  mind  on  the  subject  and  think  about  it.  Newton 
said  he  made  his  great  discoveries  by  continually  thinking 
about  them.  We  should  surround  the  subject  of  thought  with 
questions.  Asking  questions  is  one  of  the  doors  to  all  great  dis- 
coveries in  science  or  inventions  in  art.  We  should  try  to  answer 
our  own  questions.  This  will  give  activity  to  our  thoughts, 
and  afford  us  something  to  say  on  the  subject.  Thus,  if  the 
subject  is,  "The  Stars,"  we  may  inquire, — What  are  stars? 
Whence  do  they  come  ?     Why  do  they  shine  at  night  ?     Why 


310  METHODS    OF    TEACHING 

do  they  twinkle  ?  With  what  have  they  been  compared  ?  etc 
The  answering  of  these  questions  will  give  a  large  amount 
of  material  for  a  composition  on  "The  Stars." 

Many  subjects  should  be  developed  around  some  leading 
tiiought,  and  we  should  endeavor  to  find  this  leading  thought, 
which  gives  unity  to  the  treatment.  The  leading  thought  of 
a  discourse  is  the  germ  from  which  it  is  developed.  It  is 
the  living  principle  from  which  it  grows;  the  parent  idea 
which  becomes  the  source  of  its  life  and  growth,  and  without 
which  the  words  will  be  but  a  dead  letter.  When  the  germ- 
thought  appears  in  the  mind,  let  the  understanding  brood 
over  it,  and  it  will  develop  into  a  living  organism  of  thought 
and  expression.  This  leading  thought  once  in  the  mind,  will 
give  rise  to  many  other  thoughts  connected  with  it,  and  which 
grow  out  of  it  as  the  branches  shoot  forth  from  the  main  stem 
of  a  tree.  If  this  general  conception  does  not  occur  at  first, 
fix  the  mind  on  the  ideas  that  do  occur,  compare  them  and 
see  what  principal  thought  they  suggest  or  lead  to,  and  thus 
reach  the  germinal  princii)le  of  the  composition,  going  from 
the  parts  to  the  whole. 

It  is  proper  also  to  think  out  some  figures  of  rhetoric,  some 
com})arisons,  similes,  or  metaphors  to  be  used  in  the  ami>lifi- 
cation  of  the  material.  Many  such  thoughts  will  occur  to  us 
in  writing,  and  they  are  usually  most  appropriate  when  thus 
suirofested  ;  but  some  of  our  best  writers  mark  down  their 
happy  thoughts  to  be  worked  into  their  productions  as  they 
are  needed. 

Reading. — The  writer  may  also  read  books  written  upon  or 
touching  upon  the  subject.  Some  of  these  ideas  may  be  taken 
and  used  as  presented,  by  giving  credit  to  their  author.  Many 
of  the  thoughts  can  be  worked  up  into  new  forms,  so  that  they 
will  be,  in  a  certain  sense,  one's  own  property.  Such  an  exer- 
cise will  be  of  great  value  to  a  young  writer,  in  teaching  hirn 
how  to  think.  In  reading,  however,  one  should  digest  and 
assimilate  what  he  reads,  so  that  it  will  appear  with  the  stamp 


TEACHING   COMPOSITION.  311 

of  his  own  mind  upon  it.     It  will  then  become  his  own  prop 
erty  and  can  be  used  at  his  will. 

Another  suggestion  in  obtaining  the  material  by  reading,  is 
to  read  authors  who  have  written  on  the  subject  or  a  kindred 
one,  and  mark  down  the  ideas  which  their  thoughts  suggest 
to  the  mind.  Many  authors  are  very  suggestive  of  ideas. 
They  seem  to  deal  in  seed-thoughts  which  fall  into  the  mind 
and  produce  other  thoughts  in  abundance.  As  we  read,  an 
idea  seems  to  spring  up  in  the  mind  by  a  sudden  illumination, 
as  the  spark  darts  from  the  flint  when  struck  b}"^  the  steel. 
Thus  Emerson  and  Carlyle  can  be  most  profitably  read  with  a 
pencil  in  the  hand,  marking  down  the  ideas  which  spring  up 
in  the  mind  as  the  eye  passes  over  the  printed  page. 

The  facts  of  biograph}-,  history,  etc.,  should  be  rallied 
around  the  leading  ideas  to  support  or  prove  the  position 
taken.  These  facts  may  be  culled  out  from  the  store-house 
of  memory,  or  we  may  go  to  books  and  gather  the  material 
needed  for  illustration  or  proof.  It  is  well  for  the  student  to 
liave  a  "commonplace  book,"  and  mark  down  such  incidents 
and  historic  statements  as  he  thinks  may  be  of  use  to  him  in 
writing. 

Collect  Material. — This  material  should  be  written  down 
on  paper,  as  it  presents  itself  to  the  mind.  It  is  well  to  have 
a  blank  book  and  jot  down  the  thoughts  as  they  may  occur 
to  us,  without  respect  to  vmy  particular  order.  This  can  be 
done  at  odd  times  as  the  thoughts  present  themselves,  so 
that  when  the  time  comes  to  write  composition,  there  wiU  be 
a  fund  of  material  to  make  use  of. 

The  Analtjsis. — The  material  having  been  acquired,  the 
pupil  should  examine  it,  see  what  is  most  interesting  or  most 
pertinent  to  the  subject,  bring  together  those  parts  that  are 
similar,  and  make  a  complete  outline  of  the  method  and  order 
of  treatment.  This  is  called  forming  the  plan,  or  the  Analy- 
sis: and  is  an  important  part  of  the  composition.  As  a  rule, 
it  should  never   be  omitted ;    the   pupil  should  always  have 


312  METHODS   OF   TEACHING. 

some  general  idea  of  the  composition  before  he  begins  to  write. 
In  a  kind  of  fancy  writing,  we  may  give  free  rein  to 
thought  and  imagination,  and  allow  them  to  play  with  the 
ideas  that  may  chance  to  present  themselves.  The  light  and 
gossipy  essays  of  Addison  and  Lamb  could  never  have  been 
written  from  an  outline,  though  even  in  many  of  these  there 
is  a  leading  idea  that  gave  shape  to  the  production.  It  is  an 
excellent  exercise  for  the  pupil  to  take  ditferent  subjects  and 
merel}'  prepare  outlines  of  their  treatment. 

In  forming  the  analysis,  the  composer  should  have  in  his 
mind  an  idea  of  what  he  wants  to  present.  If  the  object  is 
description,  he  should  see  clearly  the  order  in  which  the  facts 
should  be  stated  to  secure  the  interest  of  the  narrative.  If 
the  production  is  reflective,  he  should  knov;  what  he  desires 
to  prove  or  to  impress,  and  arrange  the  points  in  such  a  way 
as  best  to  secure  this  object.  Care  should  be  taken  that  there 
be  no  abrupt  breaks  between  the  parts,  but  that  one  part  flows 
naturally  out  of  and  into  another.  It  will  be  well  sometimes 
to  tr\'  diff"erent  arrangements,  and  see  which  seems  best.  A 
writer  will  often  change  the  whole  plan  of  his  essay  while  he 
is  writing  it  out,  as  a  general  changes  his  plan  of  attack  on 
the  field  of  battle ;  but  this  is  alwaj's  inconvenient  and  haz- 
ardous. A  very  great  deal  of  good  judgment  may  be  shown 
in  the  analj'sis  of  subjects,  and  the  success  of  a  lecture  or  ad- 
dress is  often  largel}'  due  to  the  arrangement  of  its  parts. 

The  Anipliflcation. — Having  formed  the  plan  of  the  com- 
position, the  next  step  is  the  Amplification.  The  facts  and 
thoughts  are  to  be  presented  in  an  orderlj'  manner;  care  is  to 
be  taken  that  the  sentences  are  clear  and  correct,  that  the 
matter  is  properly  connected,  that  the  style  is  suited  to  the 
■subject,  etc.  Many  new  ideas  and  illustrations  will  present 
themselves  in  the  course  of  the  ami^lification;  and  when  ap- 
propriate should  be  wrought  into  the  composition. 

There  are  three  parts  of  a  literarj'  production  that  require 
esj>ecial  attention.     These  are  the  Introduction,  the  Body,  and 


TEACHING   COMPOSITION.  813 

the  Close.  In  an  ordinarj'^  short  school  essay,  these  divisions 
are  not  so  marked ;  and  3'et  the}'  are  not  to  be  overlooked  even 
there.  Every  production  should  have  a  fitting  opening  and 
closing  thought;  it  should  neither  open  nor  close  with  an 
awkward  abruptness.  In  lengthy  essays,  lectures,  orations, 
etc.,  these  divisions  should  be  distinctly  marked. 

The  Introduction — The  Introduction  should  be  modest, 
appropriate,  lively,  and  interesting.  It  should  not  promise  too 
much,  or  the  expectations  it  raises  may  be  disappointed.  It 
should  grow  naturally  out  of  the  subject,  and  be  a  natural  in- 
troduction to  what  is  to  follow.  It  should  be  suited  to  attract 
r.otice,  and  to  prepare  the  mind  to  listen  with  attention  and 
an  expectation  of  pleasure  to  what  follows.  An  interesting 
incident,  an  apt  illustration,  a  humorous  remark,  etc.,  are 
often  used  b^'  good  writers  and  speakers  as  an  introduction. 
In  an  oration,  the  introduction  should  li:ive  an  air  of  candor 
and  modest}- ;  it  should  be  calm  and  moderate,  and  not  antici- 
pate the  main  points  of  the  discussion. 

Cicero  laid  down  the  rule  that  the  Introduction  should  be 
written  last,  though  he  did  not  always  follow  his  own  precept. 
He  was  accustomed  to  prepare  introductions  and  lay  them 
aside  to  be  used  when  needed.  On  one  occasion,  he  inadver- 
tently used  the  same  introduction  twice  ;  and  upon  being  in- 
formed of  it  by  Atticus,  he  confessed  his  error,  and  prepared 
a  new  one. 

The  Body. — In  the  Body  of  the  essay,  the  subject  should  be 
formally  developed.  The  leading  idea  should  be  kept  care- 
fully in  mind,  and  the  etfort  be  made  to  unfold  it.  There 
should  be  an  organized  growth  of  thought  and  expression  in 
■which  all  the  subordinate  ideas  are  gathered  around  the  prin- 
cipal one.  A  thread  of  related  thought  should  run  unbroken 
through  the  entire  exposition,  binding  all  the  parts  together 
in  symmetry  and  unity. 

In  view  of  this,  the  ditferent  points  to  be  presented  should 
be  arranged  in  the  best  order.     If  there  are  objections  to  be 
14 


314  METHODS    OF   TEACHING. 

answered,  it  is  usually  best  to  attend  to  them  first.  Having 
cleared  the  way  of  these,  the  direct  arguments  may  then  be 
presented,  throwing  the  less  plausible  ones  in  the  middle,  and 
thus  giving  the  stronger  ones  first  and  last.  The  exhortation 
and  appeal  to  the  feelings  come  appropriately  toward  the 
close,  but  an  incidental  appeal  may  be  made  at  different  times 
as  the  occasion  offers. 

If  humorous  passages  occur  in  a  spoken  discourse,  they 
should  not  come  in  too  near  the  beginning,  or  they  will  unfit 
the  minds  of  the  hearers  to  listen  to  what  follows.  So  also  it 
is  not  well  to  touch  the  feelings  with  pathos  near  the  early 
part  of  the  discourse,  for  it  will  be  difficult  to  hold  the  inter- 
est after  the  reaction  of  feeling  takes  place.  It  is  well  also 
that  the  production  should  increase  in  majesty  and  grandeur 
of  exi)ressi()n  towards  its  close. 

Care  should  be  taken  that  the  thoughts  be  expressed  in  an 
attractive  and  pleasing  form.  The  language  should  be  simple, 
clear,  and  impressive.  When  suitable,  it  may  be  adorned 
with  fio;ures  of  rhetoric  and  pictures  of  the  imagination. 
Nothino;  should  be  introduced,  however,  for  mere  ornament, 
and  that  does  not  contribute  to  the  main  purpose  of  the 
essay.  Much  self-denial  is  often  retjuired  to  avoid  putting 
words  or  figures  into  a  production  when  their  only  claim  is 
their  beauty.  It  is  in  this  that  the  difference  between  a  culti- 
vated and  an  uncultivated  writer  is  readily  noticed. 

The  Conclusion. — The  Conclusion,  or  Peroration  of  a  dis- 
course, like  the  Introduction,  requires  especial  care.  The 
object  is  to  leave  as  deep  an  impression  on  the  mind  of  the 
reader  or  listener  as  possible.  This  is  sometimes  done  by  re- 
serving the  strongest  or  most  impressive  head  of  the  discourse 
for  the  last,  and  ending  with  it.  Sometimes  the  writer  or 
speaker  gives  a  brief  and  striking  summary  of  the  whole  dis- 
course, bringing  it  all.  in  rapid  succession,  again  before  the 
mind.  In  this  way  the  conclusion  becomes  a  kind  of  burning- 
glass  which  gathers  into  a  focal  point  all  the  separate  rays  ol 
the  production. 


TEACHING   COMPOSITION.  315 

The  conclusion  ma}'  often  consist  of  an  exhortation  or 
appeal  to  the  feelings,  in  view  of  what  had  been  stated.  Ac- 
cepting the  views  of  the  writer  or  speaker,  the  reader  or  lis- 
tener is  prepared  to  sympathize  with  his  feelings  and  to  share 
in  his  emotions.  In  every  case,  where  there  is  a  formal  con- 
clusion, it  should  seem  to  flow  naturally  out  of  the  discussion 
and  be  appropriate  to  it  and  the  subject. 

Dr.  Hart  says,  "  The  main  thing  to  be  observed  is  to  hit 
upon  the  precise  time  for  bringing  the  discourse  to  a  point. 
If  this  is  done  too  abruptly,  it  leaves  the  hearers  expectant 
and  dissatisfied.  If,  when  the  discourse  seems  ended,  and  the 
hearers  are  looking  for  the  close,  the  speaker  continues  turn- 
ing round  and  round  the  point,  without  coming  to  a  pause, 
the  audience  becomes  restless  and  tired.  There  are,  indeed, 
very  few  speakei'S  that  know  how  or  when  to  stop." 

In  this  discussion  of  composition  writing,  we  have  lifted  the 
subject  up  into  the  plane  of  preparing  a  lecture  or  an  oration; 
but  it  will  be  seen  that  the  suggestions  given  nearly  all  apply 
to  the  writing  of  an  ordinary  school  composition.  A  compo- 
sition, if  thoughtful,  is  a  little  lecture  or  a  little  oration,  and 
is  designed  to  prepare  for  these  larger  productions ;  and  the 
same  methods  and  principles  that  apply  to  one  apply  also  to 
the  other,  the  difference  being  one  of  degree  only.  We  close 
the  subject  with  a  few  general  suggestions. 

III.  General  Suggestions. — There  should  be  frequent  ex- 
ercises in  writing  composition.  In  many  schools  pupils  are 
required  to  write  once  in  two  weeks.  It  would  be  better, 
however,  to  have  them  write  every  week;  and  still  better  to 
have  the  exercise  more  frequently. 

Paper,  Writing,  etc. — The  pupils  should  be  required  to 
write  on  paper  of  a  uniform  size.  The  large-sized  letter- 
paper,  known  as  "  Bath  post,"  is  perhaps  the  most  convenient. 
The  subject  should  be  written  at  the  top  of  the  page  on  the 
middle  of  the  first  line ;  and  a  blank  line  left  between  the 
heading  and  the  composition.     There  should  be  a  margin  of 


816  METHODS   OF  TEACHING. 

about  one  inch  on  the  left-hand  side  of  each  page,  to  allow 
room  for  corrections.  The  first  line  of  each  paragraph  should 
be  indented  about  one  inch.  The  writing  should  be  neat  and 
legible,  with  no  flourishing  or  fancy  writing ;  and  care  should 
be  taken  with  respect  to  the  paragraphs,  etc.  The  signature 
should  be  written  on  the  next  line  below  the  close  of  the  com- 
position, near  the  right-hand  edge;  and  tiie  name  of  the  place 
and  date  on  the  next  line  below  the  signature,  near  the  left- 
hand  edge.  The  compositions  should  all  be  folded  alike,  in 
three  divisions;  and  the  name  of  the  writer,  the  subject,  and 
the  date,  be  written  on  the  back.  If  an  outline  is  required, 
it  may  be  written  either  at  the  beginning  or  close  of  the 
composition. 

Corrections. — The  compositions  should  be  handed  in 
promptl^"^  at  the  time  appointed,  for  correction.  The  correc- 
tions, as  a  rule,  should  be  made  b}' the  teacher;  though  at 
times  the  essiA^s  may  be  distributed  among  the  members  of 
the  class  for  correction,  under  the  general  supervision,  how- 
ever, of  the  teacher.  The  corrections  may  include  errors  in 
orthography,  punctuation,  use  of  capitals,  hyphens  and  apos- 
trophes, construction  of  sentences,  figures  of  rhetoric,  style 
of  expression,  general  development  of  the  subject,  etc.  The 
closeness  of  the  correction  should  be  adapted  to  the  age  and 
ability  of  the  pupils.  Severe  criticism  will  tend  to  discourage 
young  pupils,  who  are  especially  sensitive  in  respect  to  their 
own  compositions. 

It  will  be  best  for  the  teacher,  as  a  rule,  to  indicate  the 
errors,  rather  than  to  correct  them,  requiring  the  pupils  to 
make  the  correction.  This  will  make  a  deeper  impression 
upon  the  mind  than  when  the  teacher  makes  the  corrections 
for  them,  and  will  lead  them  to  be  more  careful  not  to  repeat 
the  mistake.  In  order  to  indicate  the  errors,  some  system  of 
notation  should  be  used.  A  line  may  be  drawn  under  each 
error,  and  the  sj-mbol  indicating  the  nature  of  it  be  written  in 
the  margin.     TL.e  notation  used  in  our  own  school,  is  as  fol- 


TEACHING   COMPOSITION.  317 

lows:  ^  for  analysis;  0,  orthography  ;  (?,  grammar;  TT,  wrong 
word ;  S,  sentence ;  P,  punctuation ;  etc.  For  a  fuller  statement 
of  the  system,  see  Westlake's  Three  Thousand  Practice  Words. 

The  teacher  may  sometimes  take  the  compositions  into  the 
class  and  call  attention  to  the  errors,  withholding  the  name  of 
the  writer,  if  he  chooses,  and  invite  corrections  and  sug- 
gestions. The  pupils  may  also  be  required  to  read  the  errors 
marked,  and  correct  them  orallj^,  or  write  them  upon  the 
board  with  their  correction.  Some  teachers  require  i)upils  to 
copy  the  composition  in  a  book  provided  for  the  purpose,  with 
the  mistakes  all  corrected. 

Reading  Compositions — There  should  be  a  time  set  apart 
for  the  reading  of  compositions.  This  is  a  very  useful  exer- 
cise, and  may  be  made  the  means  of  a  great  deal  of  literary 
culture.  In  this  exercise,  each  pupil  may  read  his  own  pro- 
duction, or  one  may  read  for  another,  as  the  pupils  or  teacher 
may  pi'efer.  After  the  reading  of  a  composition,  remarks  and 
criticisms  may  be  made,  first  by  the  pupil  and  then  by  the 
teacher.  Care  should  be  taken  that  the  attitude,  expression, 
etc.,  of  the  reader  be  free  from  error.  Pupils  may  often  be 
required  to  commit  their  essays  and  recite  or  declaim  them, 
those  designed  for  declamation  being  written  in  the  style  of 
an  oration. 

The  exercises  of  "composition  day"  may  be  made  very  in- 
teresting and  instructive  by  varied  literary  exercises.  A 
paper,  with  an  appropriate  name,  to  which  the  pupils  contrib 
ute,  will  give  variety  to  their  productions  and  be  of  great 
interest  to  the  pupils.  It  may  contain  short  essays,  editorials, 
items  of  news,  amusing  incidents,  wit,  humor,  poetry,  adver- 
tisements, etc.  Some  orations,  recitations,  dialogues,  and 
debates  will  also  give  additional  interest  to  the  occasion. 
The  class  may  occasionally  be  resolved  into  a  literary  society 
with  regular  officers  and  a  programme  of  exercises,  consisting 
of  an  inaugural  address,  orations,  recitations,  essays,  answera 
to  referred  questions,  a  paper,  etc. 


318  METHODS   OF   TEACHING. 

In  convjlusion,  we  remark  that  the  teacher  should  spare  nc 
pains  to  create  an  interest  in  literary  culture.  No  greater 
intellectual  benefit  can  be  conferred  upon  a  pupil  than  to  cul- 
tivate in  him  a  literary  taste  and  train  him  to  an  appreciation 
of  literary  productions.  That  teacher  achieves  a  great  success 
and  accomplishes  a  valuable  work,  who  makes  composition 
writing  a  pleasing  task  and  composition  day  to  be  regarded 
with  interest  and  delight. 


MATHEMATICS. 


CHAPTER  I. 

THE   NATURE    OF    MATHEMATICS. 

MATHEMATICS  is  the  science  of  Quantit3\  It  seeks  to 
ascertain  the  relations  and  truths  of  quantity,  and  to  de- 
rive unknown  quantities  from  other  quantities  that  are 
known.  This  definition  indicates  the  general  nature  of  the 
subject,  tliough  it  is  not  entirely  free  from  objections.  Many 
attempts  have  been  made  to  frame  a  philosophical  definition 
of  mathematics,  but  none  has  yet  been  presented  which  is  gen- 
erally acceptable. 

The  term  Mathematics  is  derived  from  the  Latin  mathemat- 
ical or  the  Greek  mathematike,  which  comes  from  mathesis, 
learning.  The  use  of  the  word  in  the  plural  form  indicates 
that  this  department  of  knowledge  was  formerly  considered 
not  as  a  single  branch,  but  as  a  group  of  several  branches, 
similar  to  our  use  of  the  phrase,  the  mathematical  sciences. 
Previous  to  the  present  centuiy,  nouns  ending  in  ics,  as 
optics,  mechanics,  etc.,  were  construed  with  a  verb  in  the 
plural ;  but  they  are  now  generally  regarded  as  singular. 

The  fundamental  branches  of  mathematics  are  Arithmetic 
and  Geometry.  This  classification  arises  from  the  nature  of  the 
two  kinds  of  quantity  considered.  The  two  general  divisions 
of  quantity  are  Number  and  Extension :  the  science  of  number 
is  Arithmetic;  the  science  of  extension  is  Geometry.  These 
two  branches  have  also  been  distinguished  with  respect  to 
their  relation  to  Time  and  Space.  Extension  has  its  origin 
in  Space,  and  number  in  Succession,  which  is  only  possible  in 
Time.     Hence,  Geometry  has  been  called  the  science  of  Space, 

(319) 


320  METHODS   Oy   TEACHING. 

and  Arithmetic  the  science  of  Time.  Geometry  has  also  been 
called  the  science  of  Form,  since  it  treats  of  the  possible 
forms  of  space. 

If  we  inti'odnce  general  symbols  for  numbers,  and  develop 
a  science  with  them,  we  iiave  another  branch  of  mathematics, 
called  Algebra.  If  we  use  these  general  symbols  in  investi- 
gating geometrical  magnitudes,  we  obtain  another  branch 
called  Analytical  Geometry.  If  we  investigate  quantity  by 
considering  the  infinitesimal  elements  of  which  it  is  com- 
posed,  we  obtain  a  branch  called  Differential  and  Integral 
Calculus. 

There  is  another  method  of  conceiving  the  subject  of  quan- 
tity and  reaching  a  division  of  the  science.  Quantity  is  of 
two  kinds;  discrete  and  continuous.  Discrete  quantity  is 
that  which  exists  in  separate  parts,  forming  quantity  of 
multitude  or  number;  as  a  number  of  men,  trees,  etc.  Con- 
tinuous quantit}'  is  that  which  daes  not  exist  in  separate 
parts,  or  is  that  in  which  the  parts  are  connected  together  in 
one  whole,  as  length,  time,  etc.  Discrete  quantity  is  immedi- 
ately expressed  in  numbers,  and  gives  rise  to  the  science  of 
arithmetic.  Continuous  quantity  cannot  be  immediately  ex- 
pressed in  numbers;  a  part  of  the  quantity  must  be  taken  as  a 
unit  of  measure  in  order  to  express  it  numerically.  One  form 
of  continuous  quantity,  that  which  belongs  to  space,  gives 
rise  to  the  science  of  geometry. 

There  is  no  general  agreement  among  writers  in  respect  to 
the  philosophical  division  of  the  science  of  mathematics. 
Comte,  the  most  celebrated  writer  on  the  philosophy  of 
mathematics,  divides  the  science  into  two  parts;  Concrete 
Mathematics  and  Abstract  Mathematics.  Under  Concrete 
Mathematics  he  includes  Geometry  and  Rational  Mechanics ; 
under  Abstract  Mathematics  he  includes  the  Calculus,  which 
embraces  Arithmetic,  or  the  Calculus  of  Values,  and  Algebra, 
or  the  Calculus  of  Functions.  The  latter,  called  also  Analy- 
sis, embraces  ordinary  algebra,  in  which  the   equations  arc 


THE   NATURE   OF    MATHEMATICS.  321 

directly  established  between  the  magnitiidos  under  considera- 
tion, and  the  Transcendental  Analysis,  in  wliich  the  desired 
equations  are  derived  by  invariable  analytic  methods  from 
equations  between  quantities  indirectly  connected  with  those 
of  the  ppoblem.  These  are  distinguished  as  the  Calculus  of 
Direct  Functions  and  the  Calculus  of  Indirect  Functions. 

3Iaterials. — A  knowledge  of  mathematics  consists  of 
Ideas  and  Truths.  The  Ideas  of  mathematics  represent  the 
different  forms  of  quantity  which  present  themselves  for  con- 
sideration. The  Truths  of  mathematics  are  the  relations  that 
exist  between  the  quantities.  When  we  conceive  and  examine 
the  different  forms  of  quantity,  we  perceive  some  truths  that 
ai'e  self-evident;  such  truths  are  called  axioms.  By  means  of 
these  axioms  we  compare  the  different  quantities,  and  attain  to 
other  truths;  these  truths  are  said  to  be  derived  by  reasoning. 
The  ideas  and  axioms  are  thus  the  basis  upon  which,  b}'  the 
process  of  reasoning,  we  build  up  the  science  of  mathematics. 

The  Ideas. — The  Ideas  of  mathematics  are  not  merel}^  ideas 
or  products  of  the  mind.  The}^  represent  realities,  things 
which  have  an  objective  existence.  The}'  are  not  ideas  of 
material  things,  there  is  no  tangible  reality  corresponding  to 
them,  but  they  are  real  forms  of  space  and  number.  The 
forms  of  geometry  are  pure  forms,  forms  not  filled  with  con- 
tent; and  the  numbers  of  arithmetic  are  pure  numbers,  inde- 
pendent of  any  association  with  material  things.  But  in  both 
cases  the  quantities  are  realities  which  admit  of  application 
to  the  objects  of  the  material  world. 

Definitions. — The  description  of  the  ideas  of  mathematics 
in  clear  and  exact  language  gives  rise  to  the  Definitions  of 
the  science.  The  Definitions  of  mathematics  may  thus  be  re- 
garded as  the  precise  description  of  its  ideas.  The  ideas  are 
antecedent  to  the  definitions,  and  are  the  basis  of  them.  In 
teaching  the  science,  definitions  are  employed  to  lead  the  mind 
of  the  learner  to  clear  conceptions  of  the  ideas.  On  account 
of  the  intimate  relation  be'  ween  the  idea  and  the  definition, 
14* 


322  METHODS   OF   TEACHING. 

some  writers  state  that   the   foundation   of  mathematics  is 
definitions  and  axioms,  rather  than  ideas  and  axioms. 

Axioms. — The  Axioms  of  mathematics  are  the  self-evident 
truths  of  the  science.  They  are  intuitive  truths  which  arise 
in  the  mind  immediately  on  the  contemplation  of  the  various 
forms  of  quantity,  without  any  process  of  reasoning.  They 
express  a  self-evident  and  necessary  relation  between  quanti- 
ties, and  thus  involve  a  comparison  or  a  judgment.  Given 
the  several  conceptions,  and  the  truth  is  immediately  per- 
ceived by  a  direct  comparison,  without  any  intervening  pro- 
cess of  thought. 

Axioms  are  the  basis  of  mathematical  reasoning.  Without 
some  self-evident  truths  as  a  starting  point,  no  process  in 
thought  is  possible.  By  some  they  are  regarded  as  general 
truths  which  contain  the  particular  truths  of  the  science,  and 
from  which  the  particular  truths  are  evolved  b^'  reasoning. 
It  seems  more  correct,  however,  to  regard  them  as  laws  which 
direct  or  govern  the  comparisons  of  the  reasoning  process. 
Thus  the  truth  that  "things  that  are  equal  to  the  same  thing 
are  equal  to  one  another,"  is  a  law  to  guide  us  in  comparing 
quantities,  rather  than  a  general  truth  that  contains  the  other 
truths  of  mathematics. 

Reaaoning. — The  Reasoning  of  mathematics  is  deductive. 
It  deals  with  necessary  truth,  and  derives  the  relations  by 
universal  and  necessary'  laws  of  inference.  The  basis  of  the 
reasoning  is  the  definitions  and  axioms,  or  in  other  words,  the 
conceptions  and  the  self-evident  truths  arising  out  of  these 
conceptions.  Thus  having  a  conception  of  a  triangle  and  a 
right  angle,  we  may  b}'  comparison,  in  accordance  with  the 
laws  of  inference,  derive  the  truth  that  "the  sum  of  the 
angles  of  a  triangle  equals  two  right  angles."  So  in  arith- 
metic, having  a  conception  of  some  subject,  as  the  greatest 
common  divisor,  we  can  derive  a  method  of  obtaining  the 
greatest  common  divisor  of  two  numbers,  gi  iding  the  inA'csti- 
gation  by  the  self-evident  truths  that  pertain  to  the  subject 


THE   NATURE    OF    MATHEMATICS.  323 

Value  of  Matltematlcs. — Mathematical  studies  have  iu 
all  ages  been  valued  for  the  mental  discipline  they  atford. 
There  is  probably  no  single  study  pursued  in  the  schools 
which  develops  the  mind  in  so  man}'  wa^'s,  and  is  so  well 
adapted  to  every  stage  of  mental  growth  as  mathematics. 
Mathematical  studies  give  some  culture  to  perception  and 
memor}',  faculties  which  it  has  been  thought  the}-  almost 
entirely'  neglect.  They  require  the  most  complete  mental 
concentration,  and  thus  aftbrd  the  highest  culture  to  atten- 
tion. Dealing  with  the  relations  of  quantity,  they  give  con- 
stant exercise  to  the  judgment,  and  train  it  to  the  closest 
discrimination  of  similarity  and  ditferences.  Every  derived 
truth  is  a  logical  deduction  from  premises,  and  is  reached  by 
the  continued  operation  of  the  power  of  reasoning.  The  first 
truths  are  axiomatic,  and  are  comprehended  only  in  an  act  of 
intuition,  which  gives  exercise  to  the  Reason. 

The  Imagination  is  also  active  in  geometry  in  picturing  the 
parts  of  the  figures  upon  which  we  reason,  and  in  creating 
diagrams  to  discover  new  relations.  All  the  definitions  are 
"logical  definitions,"  and  as  such  train  to  the  nicest  percep- 
tion of  the  relation  between  ideas  and  their  expression.  In 
fact  there  is  no  one  science  that  brings  so  large  a  number  of 
the  faculties  of  the  mind  into  so  constant  and  forcible  an 
activity,  and  especiallj^  those  faculties  which  give  strength 
and  dignit}'  to  the  intellect,  and  glory  to  scientific  achieve- 
ment. That  it  does  not  train  to  habits  o^  probable  reasoning, 
and  does  not  give  facts  for  induction  and  for  oi)inions  on 
social  and  political  questions,  is  admitted;  but  that  it  does 
more  than  any  other  school  study  to  give  mental  power  and 
logical  habits  of  thought,  must  also  be  admitted. 

Eleinentary  Urauches. — The  three  elementary  branches  of 
mathematics  are  Arithmetic,  Algebra,  and  Geometry.  These 
are  taught  in  all  our  graded  and  high  schools,  and  should,  in 
their  elements  at  least,  be  taught  in  the  ordinary  common 
schools.  We  shall  in  this  work  discuss  the  methods  of  teach- 
inji  these  three  branches. 


CHAPTER  II. 

THE  NATURE  OF  ARITHMETIC. 

THE  science  of  arithmetic  is  one  of  the  purest  products  of 
human  thought.  It  was  aided  in  its  growth  by  the  rarest 
minds  of  antiquity',  and  enriched  b\'  tlie  thought  of  the  pro- 
foundest  thinkers.  Over  it  P^'thagoras  mused  with  the 
deepest  enthusiasm;  to  it  Plato  gave  the  aid  of  his  refined 
speculations ;  and  in  unfolding  some  of  its  truths  Aristotle 
emplo3'ed  his  peerless  genius.  In  its  processes  and  principles 
shines  the  thought  of  the  ancient  and  modem  world ;  the 
subtle  mind  of  the  Hindoo,  the  classic  culture  of  the  Greek, 
and  the  practical  spirit  of  the  Italian  and  Englishman.  It 
comes  to  us  adorned  with  the  offerings  of  a  thousand  intel- 
lects, and  sparkling  with  gems  of  thought  received  from  the 
great  minds  of  nearly  every  age. 

Like  all  science,  which  is  an  organic  unity  of  truths  and 
principles,  the  science  of  arithmetic  has  its  fundamental 
ideas,  out  of  which  arise  subordinate  ones,  which  themselves 
give  rise  to  others  contained  in  them,  and  all  so  related  as  to 
give  sj-mmetry  and  proportion  to  the  whole.  These  funda- 
mental and  derivative  ideas,  the  law  of  their  evolution,  and 
the  philosophical  thread  that  runs  through  them  and  binds 
the  parts  together  into  an  organic  unity,  should  be  understood 
by  the  teacher. 

To  aid  the  teacher  in  acquiring  a  more  philosophic  concep- 
tion of  arithmetic  than  he  obtains  from  the  text-book,  we  shall 
speak  of  the  General  Nature  of  the  science,  its  Language, 
Reasoning,  and  Methods  of  Treatment.  We  shall  then  pro- 
ceed to  consider  the  Methods  of  Teaching  the  subject. 

(324)'    ■ 


NATURE   OF   ARITHMETIC.  325 


I.  The  General  Nature  of  Arithmetic. 

Definition. — Arithmetic  is  the  science  of  numbers  and  the 
art  of  computing  with  them.  The  term  is  derived  from 
arithmetike,  which  is  from  arithmos^  meaning  number.  This 
is  the  definition  usually  given,  and  is  sufficiently  correct  for 
all  practical  purposes.  There  are  some  writers,  however,  who 
hold  that  Arithmetic  is  only  one  of  the  sciences  of  numbers, 
Algebra  and  Calculus  being  also  regarded  as  sciences  of  num- 
ber Some  French  writers  call  the  general  science  of  numbers 
Numerique ;  and  divide  it  into  Arithmetic,  the  science  of 
special  numbers,  and  Algebra,  the  science  of  number  in  gen- 
eral.    Sir  Isaac  Newton  called  algebra  Universal  Arithmetic. 

The  Nature  of  Nuuiher. — The  basis  of  arithmetic  is 
Number.  A  number  is  usually  defined  as  a  unit  or  a  collec- 
tion of  units,  a  definition  derived  from  Euclid.  This  definition 
is  liable  to  the  objection  that  a  number  and  a  collection  are  not 
quite  identical  in  meaning.  Many  definitions  of  a  Number 
have  been  attempted,  but  none  has  yet  been  given  which  is 
entirely  satisfactory  to  mathematicians.  The  simple  idea  of 
a  number  is  that  it  is  the  how-many  of  a  collection  of  objects, 
and  it  might  be  so  defined.  The  definition  first  given  is, 
however,  the  one  generally  preferred  by  writers  on  arithmetic. 

There  are  three  fundamental  classes  of  numbers  ;  Integers, 
Fractions,  and  Denominate  Numbers.  These  three  classes  arc 
practically  and  philosophically  distinguished,  and  constitute 
the  basis  of  a  threefold  division  of  the  science.  Logically  the 
distinction  is  not  entirely  without  exception,  since  a  fraction 
may  be  denominate,  and  a  denominate  number  may  be  inte- 
gral; but  the  division  is  regarded  as  philosophical,  since  these 
three  classes  of  numbers  not  only  differ  in  character,  but  re- 
quire distinct  methods  of  treatment,  and  give  rise  to  distinct 
rules  and  processes. 

Integers. — An  Integer  is  a  number  of  integi'al  units.    These 


326  METHODS   OF   TEACHING. 

units  are  regarded  as  iudividual  or  whole,  and  hence  an  Inte- 
ger is  called  a  whole  number.  There  is  no  relation  of  the 
things  numbered  to  an^-  other  thing  regarded  as  a  unit;  but 
simply  the  relation  of  the  collection  to  a  single  thing  of  the 
collection.     An  integer  is  thus  a  pure  product  of  synthesis. 

Fractions. — The  Unit,  as  the  basis  of  arithmetic,  may  be 
multiplied  or  divided.  A  synthesis  of  units,  as  we  have  seen, 
gives  rise  to  Integers;  a  division  of  the  Unit  gives  rise  to 
Fractions,  Dividing  the  unit  into  a  number  of  equal  parts, 
we  see  that  these  parts  bear  a  definite  relation  to  the  integral 
unit,  and  name  them  from  this  relation.  These  parts  mHy  be 
regarded  as  individual  things,  and  constitute  a  particular 
class  of  units  called  fractional  units.  The  collection  and 
numbering  of  these  fractional  units  give  rise  to  a  particular 
class  of  numbers  called  Fractions. 

Denominate  Numbers. — Quantity  is  of  two  kinds — (juantity 
oi  multitude  and  quantity  oi  magnitude — called  also  discrete 
and  continuous  quantity.  Discrete  quantity  exists  in  indi- 
vidual units  and  is  immediately  estimated  as  how  many; 
continuous  quantity  exists  in  the  mass,  and  is  primarily  esti- 
mated as  how  much.  Thus  we  say  how  many  apples,  how 
viany  trees,  etc.,  while  we  say  how  much  money,  how  much 
land,  etc.  Quantity  of  magnitude  does  not  primarily  admit  of 
numerical  expression  ;  to  thus  express  it,  we  fix  ui)on  some 
definite  part  of  the  quantity  as  a  unit  of  measure,  and  express 
the  quantity  by  the  number  of  times  it  contains  the  unit  of 
measure.  Continuous  quantity  thus  becomes  expressed  as 
discrete  quantity-;  the  how  much  is  reduced  to  the  how  many ; 
and  a  new  class  of  numbers  arises,  called  Denominate  Num- 
bers. These  units  being  of  difii'erent  sizes  and  bearing  ditier- 
ent  relations  to  one  another,  require  a  special  method  of 
treatment  which  gives  rise  to  a  distinct  department  of  arith- 
metic. With  the  adoption  of  the  metric  S3-stem,  this  part  of 
arithmetic  will  lose  the  distinctive  character  of  its  operations. 

Logical  Outline  of  A  I'ilhmctic. — The  science  of  Arithme- 


THE   NATURE    OF    ARITHMETIC.  327 

tic  is  based  upon  and  is  developed  from  these  three  classes 
of  numbers.  Its  several  parts  are  evolved  from  the  possil)le 
operations  upon  these  numbers.  A  consideration  of  tliese 
possible  operations  will  give  us  a  Logical  Outline  of  Arith- 
metic. 

All  numerical  ideas  begin  at  the  Unit.  The  Unit  is  the 
origin,  the  basis  of  arithmetic.  The  Unit  can  be  multiplied 
and  divided;  hence  arise  Integers  and  Fractions.  Each 
Integer  is  a  synthetic  product  derived  from  a  combination  of 
units  ;  each  Fraction  is  an  analytic  product  derived  from  the 
division  of  the  unit.  Having  obtained  numbers  by  a  synthesis 
of  units,  we  may  unite  two  or  more  numbers,  and  thus  obtain  a 
larger  number  by  means  of  synthesis;  or  we  may  reverse  the 
operation  and  descend  to  a  smaller  number  b}^  means  of  analy- 
sis. Hence  the  two  fundamental  operations  of  arithmetic  are 
S^aithesis  and  Analysis.  To  determine  when  and  how  to 
unite  and  separate  numbers,  we  employ  a  process  of  reasoning 
called  comparison.  This  process  compares  numbers  and  de- 
termines their  relations  ;  it  is  the  thought  process  of  arithme- 
tic, as  analysis  and  synthesis  are  the  mechanical  processes. 
Comparison  directs  the  original  processes  of  arithmetic,  mod- 
ifies them  so  as  to  produce  from  them  new  ones,  and  also  itself 
gives  rise  to  other  processes  not  contained  in  or  growing  out 
of  the  original  ones.  Comparison  is  thus  the  process  by  which 
the  science  is  constructed ;  it  is  the  key  with  which  the  learner 
unlocks  its  rich  store-house  of  interest  and  beaut^'. 

Syyithesis. — A  general  synthesis  is  called  Addition.  A 
special  case  of  the  sj'uthetic  process  of  addition,  in  which 
the  numbers  added  are  all  equal,  is  called  Multiplication. 
The  forming  of  Composite  Numbers  hy  a  synthesis  of  factors, 
which  we  call  Composition,  Multiples  formed  by  a  synthesis 
of  particular  factors,  and  Involution,  a  synthesis  of  equal 
factors,  are  all  included  under  Multiplication.  Hence  the 
process  of  Addition  includes  all  the  synthetic  processes  to 
which  numbers  can  be  subjected. 


328  METHODS   OF  TEACHING. 

Analysis. — A  general  anal3'sis,  the  reverse  of  Addition,  is 
called  Subtraction.  A  special  case  of  Subtraction,  in  which 
the  same  number  is  successively  subtracted  with  the  object  of 
ascertaining  how  many  times  it  is  contained  in  another,  is 
called  Division.  A  special  case  of  Division,  in  which  many  or 
all  of  the  makers  or  factors  of  a  number  are  required,  is  called 
Factoring  ;  a  special  case  of  Factoring,  in  which  one  of  the 
several  equal  factors  is  required,  is  called  Evolution;  and  a 
case  in  which  some  common  factor  is  required,  is  called  Com- 
mon Divisor.  Hence  the  process  of  Subtraction  includes  all 
the  analytic  processes  to  which  numbers  can  be  subjected. 

Comparison. — By  comparison  the  general  notion  of  relation 
is  attained,  out  of  which  arise  several  distinct  arithmetical 
processes.  By  comparing  numbers  we  obtain  the  idea  of 
Ratio ^  arithmetical  and  geometrical.  A  comparison  of  equal 
ratios  gives  us  Proportion.  A  comparison  of  numbers  differ- 
ing by  a  common  ratio  gives  us  Arithmetical  Progression  and 
Geometrical  Progression.  In  comparing  numbers  of  difierent 
units,  we  observe  we  may  pass  from  one  to  another  of  differ- 
ent species  under  the  same  genus,  and  thus  have  the  process 
of  Reduction.  In  comparing  numbers,  we  may  assume  some 
number  as  a  basis  of  reference,  and  develop  their  relations  in 
regard  to  this  basis  ;  when  this  basis  is  a  hundred,  we  have 
the  process  of  Percentage.  In  comparing  numbers,  we  dis- 
cover certain  relations  and  peculiarities  which  give  rise  to 
the  Properties  or  Principles  of  numbers. 

Remarks. — We  thus  derive  a  complete  outline  of  the  science 
of  numbers.  Arithmetic  is  seen  to  consist  fundamentally  of 
three  things  ;  Synthesis,  Analysis,  and  Comparison.  Synthe- 
sis and  Analysis  are  fundamental  mechanical  operations; 
Comparison  is  the  fundamental  thought-process  which  con- 
trols these  operations,  brings  out  their  potential  ideas,  and 
also  gives  rise  to  other  divisions  of  the  science  growing  out 
of  itself.  The  whole  science  of  pure  arithmetic  is  the  out- 
growth of  this  triune  basis, — Synthesis,  Analysis,  and  Com- 


THE   NATURE   OF   ARITHMETIC.  329 

parison.  The  rest  of  arithmetic  consists  of  the  solution  of 
problems,  either  real  or  theoretical,  and  may  be  included 
under  the  head  of  Applications  of  Arithmetic. 

This  outline  of  the  science  grows  out  of  the  idea  of  pure 
number,  independent  of  the  language  of  arithmetic.  These 
fundamental  processes  are  modified  by  the  method  of  nota- 
tion adopted  to  express  numbers.  With  the  Roman  or  Greek 
methods  of  notation,  the  methods  of  operation  would  not 
be  the  same  as  with  the  Arabic  sj-stem.  The  method  of 
adding  by  "  carrying  one  for  every  ten,"  of  subtraction  by 
"borrowing,"  a  portion  of  the  treatment  of  common  and  deci- 
mal fractions,  the  methods  of  extracting  roots,  etc.,  are  all 
largely  due  to  the  system  of  notation  adopted,  and  many  of 
them  have  their  origin  in  the  Arabic  S3Stem.  It  may  be 
remarked,  also,  that  the  power  of  arithmetic  as  a  calculus 
depends  upon  the  beautiful  and  ingenious  system  of  notation 
adopted  to  express  numbers. 

II.   The  Language  of  Arithmetic. 

The  expression  of  the  fundamental  ideas  of  arithmetic  givetj 
rise  to  Arithmetical  Language.  This  language  is  both  oral 
and  writt-en.  The  oral  language  is  called  Numeration ;  the 
written  language  is  called  Notation.  Numeration  is  the 
method  of  naming  numbers  and  of  reading;  them  when  ex- 
pressed  in  written  characters.  Notation  is  the  method  of 
expressing  numbers  in  written  characters. 

Numeration. — In  naming  numbers  we  do  not  give  each 
number  an  independent  name,  but  proceed  upon  the  principle 
of  naming  a  few  numbers  and  then  forming  groups  or  collec- 
tions, naming  the  groups,  and  using  the  first  names  to  num- 
ber the  groups.  This  ingenious,  though  simple  and  natural, 
method  of  naming  numbers  by  forming  groups  or  classes, 
seems  to  have  been  adopted  by  all  nations.  It  has  the  advan- 
tage of  emplo3'ing  but  a  few  names  to  express  even  very 
large  numbers,  and  of  enabling  the  mind,  by  the  principle  zf 


330  METHODS   OF   TEACHING. 

classification,  to  conceive  quite  readily  of  a  numlter  otherwise 
entirely  bej'ond  its  powers  of  conception. 

Thus,  after  naming  the  numbers  as  far  as  ten,  we  regard  the 
collection  ten  as  a  single  thing,  and  count  oh<?  and  ten,  two  and 
ten,  etc.,  up  to  twenty ;  and  then  continuing  in  the  same  way, 
we  have  two  tens  and  one,  two  tens  and  two,  etc.,  up  to  three 
tens ;  and  so  on  until  we  obtain  ten  of  these  groups  of  tens. 
These  ten  groups  we  now  bind  together  by  a  thread  of  thought 
forming  a  new  group  which  we  call  a  hundred ;  and  proceed- 
ing from  the  hundred  in  the  same  way,  we  unite  ten  of  these 
into  a  larger  group,  which  we  name  thousand,  etc.  The 
names  of  the  numbers  immediately  following  the  first  group 
are  not  (luite  in  the  form  suggested ;  but  they  involve  the 
principle  named.  Thus,  instead  of  one  and  ten,  we  say 
eleven,  from  the  Saxon  endlefen,  or  Gothic  ainlif  (ain,  one 
and  lif,  ten);  and  instead  oi  two  and  ten,  we  say  twelve,  from 
the  Saxon  twelif,  or  Gothic  tvalif  (tva,  two,  and  iif,  ten). 
The  names  of  the  numbers  following  these  have  been  modified 
and  abridged  by  use,  though  in  the  present  form  they  suggest 
the  original  expression  and  show  the  principle  of  naming 
numbers. 

Origin  of  Names. — The  origin,  or  primary  meaning  of  the 
names  applied  to  the  first  ten  numbers,  is  not  known.  It  has 
been  supposed  that  the  names  of  the  simple  numbers  were 
originally  derived  from  some  concrete  objects,  and  probaljly 
from  some  part  of  the  person.  Many  tribes  have  used  the 
term  hand  to  express  five,  aud  man  for  twenty.  Humboldt 
says  that  the  Indians  of  New  Grenada  use  ata,  water,  foro/je; 
bosa,  an  inclosure,  for  two ;  mica,  changeable,  for  three ;  etc. 
Prof.  Goldstiicker  gives  the  following  theory  for  the  origin  of 
the  Sanskrit  numerals,  and  thus  of  our  own,  which  are  de- 
rived from  the  Sanskrit :  One,  he  says,  is  "  he;"  two,  "diver- 
sity ;"  three,  "  that  which  goes  beyond ;"  four,  "  and  three," 
that  is,  "one  and  three;"  five,  "coming  after;"  six,  "aud 
four,"   that  is,   "two  and  four;"  seven,  "following;"   eiyld^ 


THE   NATURE   OF    ARITHMETIC.  331 

'•tn'O  fours  ;"  nine,  "that  which   comes  after  ;"  ten,  "  two  and 
eight  "    Thus  only  one  and  two  have  distinct  original  meanings. 

After  reaching  the  thousand  it  will  be  noticed  that  a  change 
occurs  in  the  method  of  grouping.  Prcdousl}',  ten  of  the  old 
groups  make  one  of  the  next  higher  group ;  but  after  the 
third  group,  or  thousand,  it  requires  a  thousand  of  an  old 
group  to  make  one  of  the  next  group  which  receives  a  new 
name.  Thus  a  group  of  a  thousand  thousands  is  called  a 
million;  a.  thousand  millions,  a  billion,  etc.  This  change  in 
the-  law  of  naming  groups  is  not  a  thing  of  chance,  but  of 
science  ;  as  it  is  a  matter  of  great  convenience  in  naming  the 
larger  numbers. 

yotation. — In  writing  numbers,  we  do  not  use  common 
words,  nor  have  a  special  character  for  each  number.  The 
method  of  notation  is  based  upon  the  principle  of  using  a /eu; 
characters  to  express  the  first  few  numbers,  and  expressing 
the  groups  by  the  position  of  these  characters.  The  founda- 
tion principle  is  that  of  place  value,  the  groups  being  repre- 
sented by  the  simple  device  of  place. 

This  method  seems  to  have  oinginated  among  the  Hindoos, 
and  is  now  adopted  b}'  all  civilized  nations.  It  is  usually 
called  the  Arabic  system,  from  the  fact  that  it  was  introduced 
into  .Europe  through  the  Arabs;  and  was  for  a  time  supposed 
to  have  originated  with  them.  The  methods  of  notation  used 
b}'  the  Greeks  and  the  Romans  were  much  inferior  to  that  of 
the  Hindoos,  so  much  so  that  it  was  impossible  to  employ 
the  Roman  system,  at  least,  in  calculations. 

The  invention  of  the  Arabic  system  of  notation  is  one  of 
the  greatest  achievements  of  the  human  mind.  Without  it, 
man}'  of  the  arts  would  never  have  been  dreamed  of,  and  the 
science  of  astronomy  would  still  be  in  its  cradle.  "With  it, 
man  becomes  armed  with  prophetic  power,  predicting  eclipses 
and  occultations.  determining  the  existence  of  worlds  which 
the  eye  of  the  telescope  had  never  seen,  and  marking  out  with 
unerring  accuracy  the  orbits  of  planets  and  their  position  in 
the  heavens  for  centuries  to  come. 


832  METHODS   OF   TEACHLN^G. 

Origin  of  Characters. — The  origin  of  the  characters  is  not 
deiinitel}'  known.  Three  theories  have  been  given  for  them, — 
that  of  a  combination  of  straight  lines,  that  of  a  combination 
and  modification  of  angles,  and  that  of  initial  letters.  It  has 
been  supposed  that  people  began  to  represent  numbers  by 
straight  lines,  and  that  these  might  have  been  combined  into 
our  present  Arabic  digits.  It  has  also  been  supposed  that 
angles  may  have  been  used  to  indicate  numbers,  and  that 
a  combination  of  these  might  have  been  modified  into  the 
present  forms.  Prinseps,  a  profound  Sanskrit  scholar,  thinks 
that  they  were  originally  the  initial  letters  of  the  Sanskrit 
numerals.  This  theory  is  rendered  plausible  from  the  fact 
that  the  Romans,  Greeks,  and  Hebrews  used  letters  to  repre- 
sent numbers. 

The  origin  of  the  cipher,  by  the  first  of  these  theories,  is 
accounted  for  by  supposing  it  to  have  been  represented  by  a 
circle,  suggested  by  counting  around  the  fingers  and  thumb 
held  in  a  circular  position.  By  the  second  theory,  if  charac- 
ters with  angles  represented  numbers,  a  character  with  no 
angles,  like  a  circle,  would  represent  nothing.  The  third 
theory  does  not  account  for  the  zero,  the  most  important 
character  of  them  all.  "  It  would  be  highly  important,"  says 
Max  Muller,  "to  find  out  at  what  time  the  naught  first  occurs 
in  Indian  inscriptions.  That  inscription  would  deserve  to  be 
preserved  among  the  most  valuable  monuments  of  antiquity, 
for  from  it  would  date  in  reality  the  beginning  of  true  mathe- 
matical science, — impossible  without  the  naught, — nay,  the 
besinninar  of  all  the  exact  sciences  to  which  we  owe  the  inven- 
tion  of  telescopes,  steam  engines,  and  electric  telegraphs." 

The  Numerical  Base. — The  basis  of  the  method  of  ex- 
pressing numbers  is  decimal.  This  arises  from  the  fact  that 
arithmetic  had  its  origin  in  counting  the  fingers  of  the  two 
hands.  There  are  traces  in  several  languages  of  other  numbers 
besides  ten  being  used  as  the  basis  of  the  system  of  counting  ; 
but  all  civilized  nations  have  counted  by  tens.      From  this 


THE  NATURE   OF   ARITHMETIC.  338 

general  use  of  the  decimal  scale,  it  has  been  inferred  that  it 
possesses  some  intrinsic  excellence;  3'et  the  fact  is,  that  it  is 
liable  to  many  objections,  a  few  of  which  we  will  mention. 

First,  the  decimal  scale  is  unnatural.  A  grouping  by  tens 
is  seldom  seen  in  nature  or  art.  Nature  groups  in  pairs,  in 
threesAn  fours  J  in  Jives,  and  in  sixes;  but  seldom  or  never 
by  tens.  Man  doubles,  and  triples,  and  quadruples;  he  di- 
vides into  halves,  thirds,  and  fourths  ;  but  where  does  he 
estimate  by  ^eras  or  teiiths,  outside  of  arithmetic?  There  is 
nothing  natural  about  the  matter,  except  the  fingers ;  and 
these  are  grouped  b}^  fours  instead  of  fives. 

Second,  the  decimal  scale  is  unscientific.  It  originated  by 
chance,  by  a  mere  accident.  Had  science,  instead  of  chance, 
presided  at  its  birth,  we  should  have  had  a  basis  that  would 
have  given  a  new  beauty  and  a  greater  simplicity  to  the 
admirable  system  of  arithmetical  language. 

Third,  the  decimal  scale  is  inconvenient.  This  arises  from 
the  base,  ten,  not  being  divisible  into  the  simple  fractional 
parts, — third,  fourth,  ixad  sixth.  These  fractions,  wliich  are 
in  common  use,  cannot  be  conveniently  expressed  in  the  deci 
mal  scale,  the:  fourth  requiring  two  places,  and  the  third  and 
sixth  ffivino-  interminate  decimals.  Were  the  basis  of  the 
scale  twelve  instead  of  ten,  all  these  fractions  could  be  ex- 
pressed in  a  single  place. 

A  Duodecimal  Base. — The  Duodecimal  Scale  would  be 
much  more  convenient  than  the  decimal.  This  is  especially 
apparent  in  the  expression  of  fractions  in  the  numerical  scale. 
In  the  duodecimal  scale,  we  could  express  |,  ^,  ^,  and  ^  in  a 
single  place,  while  |  and  |  would  require  but  two  places. 
Thus,  in  the  duodecimal  scale,  we  should  have  |^=.6,  ^=.4, 
i  =  .3,  |^=.2,  i=.16,  and  ^=.14.  The  fractions  I  and  }  both 
give  perfect  repetends  in  the  duodecimal  scale, — thus,  4=  .24 9 7 
and  |=. 186*35  ;  but  this  would  be  no  disadvantage,  as  these 
fractions  are  seldom  used  in  actual  life.  The  character  $  is 
used  to  express  ten,  for  both  ten  and  eleven  would  be  repre- 
sented by  a  single  cliaracter  in  the  duodecimal  scale. 


334  METHODS   OF  TEACHING. 

There  seems  to  have  been  a  natural  tendency  towards  a 
duodecimal  scale.  Thus  a  large  number  of  things  are  reck- 
oned by  the  dozen;  and  the  scale  is  even  extended  to  the 
second  and  third  degree, — to  the  g7'0ss  and  gi^eat  gross.  In 
our  naminsT  of  numbers,  the  terms  eleven  and  twelve  seem  to 
postpone  the  forming  of  a  group  until  we  reach  a  dozen.  A 
similar  fact  is  noticed  in  the  extension  of  the  multiplication 
table  to  "12  times."  The  division  of  the  year  into  twelve 
months,  the  circle  into  twelve  signs,  the  foot  into  twelve 
inches,  the  pound  into  twelve  ounces,  etc.,  are  further  indica- 
tions of  the  same  tendency. 

A  change  of  our  numerical  base  has  been  advocated.  Leib- 
nitz preferred  a  binary  base,  and  composed  a  binary  arithme- 
tic. Charles  XII.  of  Sweden  seriously  contemplated  intro- 
ducing the  duodecimal  system  into  his  dominions,  and  was 
probably  prevented  doing  so  only  by  his  early  death.  If  this 
change  could  be  made,  it  would  greatly  simplify  the  science 
of  numbers,  and  facilitate  its  applications.  For  a  fuller  dis- 
cussion of  this  subject,  see  Fhilosophy  of  Arithmetic. 

III.   The  Reasoning  of  Arithmetic. 

The  science  of  arithmetic,  like  geometry,  embraces  ideas  and 
truths.  These  ideas  give  rise  to  definitions;  and  the  truths 
are  expressed  in  axioms  and  theorems  or  principles.  The 
axioms  are  the  self-evident  truths  that  flow  out  of  our  numer- 
ical conceptions  ;  the  principles  are  derived  by  reasoning. 
These  principles  may  be  applied  in  deriving  methods  of  opera- 
tion and  in  the  solution  of  practical  problems.  The  statement 
of  the  method  of  operation  gives  us  the  rules  of  arithmetic. 

Definitions. — The  definitions  of  arithmetic  are  concise 
descriptions  of  the  ideas  of  the  science.  These  ideas  are  of 
three  different  classes.  First,  we  have  our  ideas  of  numbers 
as  quantities;  as  a  unit,  a,  fraction,  a  multiple,  etc.  Seccnd, 
we  have  ideas  of  operation;  as,  addition,  subtraction,  etc. 
Tliird,  we  have  ideas  of  relation  ;  as,  ratio^  proportion,  etc 


THE   NATURE    OF   ARITHMETIC.  335 

The  statement  or  description  of  these  several  cUisses  of  ideas, 
gives  us  the  dejinilionti  of  aritlnuetic.  The  definitions  of 
arithmetic  are  consequently  of  three  classes ;  definitions  of 
Quantit}^,  of  Operation,  and  of  Relation. 

Axioms. — The  axioms  of  arithmetic  are  the  self-evident 
truths  which  belong  to  the  subject.  They  are  of  two  classes; 
those  which  pertain  to  quantitj^  in  general  and  those  which 
pertain  to  number  in  particular.  Among  the  former  are  the 
following :  "  The  whole  is  greater  than  any  of  its  parts ;" 
"  Things  which  are  e(iual  to  the  same  thing  are  equal  to  one 
another;"  etc.  Among  the  latter  class  of  axioms  ma}'  be 
mentioned  the  following:  "Similar  numbers  only  can  be 
added;"  "The  multiplier  is  always  an  abstract  number;"  etc. 

The  arithmetical  axioms  of  the  second  class  arise  out  of  the 
particular  conceptions  of  arithmetic.  Each  new  conception 
of  a  relation  or  a  process  gives  rise  to  one  or  more  self-evident 
truths.  Thus,  as  soon  as  we  attain  the  idea  of  a  factor  as  a 
maker  of  a  number,  we  immediately  perceive  the  truth  that 
"a  factor  of  a  number  is  a  divisor  of  the  number."  Also,  as 
soon  as  we  attain  the  idea  of  a  multiple  of  a  number  as  a 
number  of  times  the  number,  we  perceive  the  self-evident 
truth  that  "a  multiple  of  a  number  contains  the  number." 

ReasoHuiff. — All  reasoning  is  comparison.  A  comparison 
requires  a  standard,  and  this  standard  is  the  Jixed,th.e  axiom- 
atic, the  known.  The  law  of  reasoning  is  to  compare  the  com- 
plex with  the  simple,  the  theoretic  with  the  axiomatic,  the  un- 
known with  the  known.  By  this  comparison  we  pass  from  the 
simple  to  the  complex,  from  the  old  to  the  new,  from  the  known 
to  the  unknoivn. 

The  reasoning  of  arithmetic  is  deductive.  The  basis  of  the 
reasoning:  is  the  ideas  and  self-evident  truths,  or  the  defini- 
tions  and  axioms.  The  definitions  present  the  forms  of  quan- 
tity about  which  we  reason;  the  axioms  present  the  truths 
which  guide  us  in  the  reasoning  process.  With  these  as  a 
basis  we  trace  our  waj'  by  comparison  from  the  simplest  truth 
to  the  profoundest  theorem. 


336  METHODS   OF  TEACHING. 

Some  writers  hold  that  there  is  no  reasoning  in  arithmetic, 
but  that  its  operations  and  principles  are  the  result  of  intui- 
tion or  immediate  judgment.  This  mistake  arises  from  sup- 
posing that  the  science  of  arithmetic  is  contained  in  and 
grows  out  of  addition  and  subtraction,  which  are  regarded  as 
purely  mechanical  processes.  Comparison  lies  at  the  basis  of 
arithmetic,  unfolds  the  two  primary  processes,  and  gives  rise 
to  other  processes  not  contained  in  addition  and  subtraction. 
The  processes  of  reasoning  in  arithmetic  can  be  reduced  to 
the  syllogistic  form  the  same  as  in  geometry.  The  demon- 
stration of  principles  in  arithmetic  can  be  made  as  logical  as 
those  in  the  science  of  form.  Besides,  if  there  were  no  reason- 
ing in  arithmetic  there  could  be  no  science  of  arithmetic. 

Arithmetical  Analysis* — One  of  the  most  common  forms 
of  reasoning  in  arithmetic  is  that  known  as  Arilhmetical 
Analysis.  It  is  a  process  of  reasoning  by  comparing  num- 
bers through  their  relation  to  the  Unit.  Assuming  that  all 
numbers  are  so  many  times  the  single  thing,  they  bear  a 
definite  relation  to  the  unit  which  is  immediately  appre- 
hended. From  this  evident  and  simple  relation  to  the  unit, 
all  numbers,  integral  and  fractional,  can  be  readily  compared 
with  one  another,  and  their  properties  and  relations  deter- 
mined. The  process  is  readily  illustrated  by  solving  the  prob- 
lem, "  If  3  times  a  number  is  18,  what  is  5  times  the  number?" 
or,  "  If  f  of  a  number  is  30,  what  is  |  of  the  number?" 

This  simple  process  of  analysis  runs  through  the  whole 
science  of  arithmetic.  It  is  its  key-note;  its  basis  principle. 
The  Unit  is  the  fundamental  idea  to  which  and  from  which 
we  reason.  It  is  a  sort  of  arithmetical  centre  around  which 
the  reasoning  process  revolves,  as  the  planets  around  their 
solar  centres.  The  process  is  called  analysis;  but  it  will  be 
noticed  that  it  contains  a  synthetic  element  also.  When  we 
pass  from  a  collection  to  the  single  thing,  that  is,  from  a 
number  to  the  unit,  the  process  is  analytic;  but  when  we  pass 
from  the  unit  to  a  number,  the  process  is  synthetic.     Both 


THE   NATURE    OF    ARITHMETIC.  337 

processes  are  included  under  the  more  general  terra  Compar- 
ison. Comparison  is  properly  ttie  thought  process;  Analysis 
and  Synthesis  are  mechanical  processes. 

TJie  Equation. — The  Equation  lies  at  the  basis  of  mathe- 
matical reasoning.  The  Equation  is  a  universal  form  of 
thought,  and,  belongs  to  arithmetic  as  well  as  to  algebra.  Tlie 
simplest  process  of  arithmetic,  '"One  and  one  are  two" 
(1  +  1  =  2),  is  really  an  equation,  as  much  so  as  x"^ -\-ax=h. 
The  equation  is  an  indispensable  element  of  arithmetical 
reasonino";  it  is  the  key  with  which  we  unlock  the  most 
complex  problems  of  the  science  of  nuuil)ers. 

The  equation  in  arithmetic  assumes  several  ditferent  forms. 
Its  primary  form  is  that  used  in  comparing  two  equal  quan- 
tities of  ditferent  form  ;  as  ix  3=6,  in  which  2x  3  is  one  form 
of  quantity  and  (5  another,  the  two  eijual  in  value,  but  involv- 
ing quite  ditferent  conceptions.  A  com[)arison  of  unequal 
quantities  gives  us  ratio,  which  may  be  expressed  in  the  form 
of  an  equation;  as  8  :  4=2.  A  comparison  of  equal  ratios 
gives  us  an  equation  of  relations,  called  a  proportion;  as 
8  :  4=12  :  6,  a  proportion  being  in  reality'  an  equation.  In 
arithmetical  analysis,  an  unknown  number  involved  with 
known  numbers  is  equated  with  known  numbers;  as  "3  times 
a  number  e</uals  24."  The  treatment  of  the  equation  in 
arithmetic  gives  rise  to  transponition  and  substitution,  as  may 
be  seen  in  arithmetical  analysis. 

That  the  equation  belongs  to  arithmetic  is  thus  evident. 
Every  formal  comparison  between  two  quantities  necessarily 
leads  to  it ;  and  such  comparisons  are  continually  made.  All 
of  our  reasoning  involves  it;  we  cannot  think  in  arithmetic 
without  the  equation.  The  mind  here  takes  its  first  steps  in 
equational  thought  which,  when  continued,  leads  to  the  high 
places  (^f  mathematical  science.  Here  the  youn^"  mind  ])lumes 
its  wiuijs  to  follow  the  great  masters  in  their  loftv  flights  in 
the  reo-ions  of  abstract  thouijht,  far  bevoud  that  to  which  tht; 
science  of  arithmetic  could  ever  attain. 
15 


338  METHODS   OF   TEACHING. 

Induction  in  Arithuiefic. — Arithmetic    is    a    deductive 
science,  and  most  of  its  truths  are  derived  by  deduction.     It 
is  possible,  however,  to  obtain  some  of  its  truths  by  induction. 
Upon  seeing  that  a  certain  thing  holds  good  in  several  cases, 
we  may  often  correctly  infer  that  it  holds  good  in  all  cases 
and  is  a  general  principle.     Thus  the  property  of  divisibility 
by  nine  may  be  presented  to  a  learner  inductively  before  he  is 
able  to  understand  a  demonstration.     The  principles  of  frac- 
tions may  also  be  derived  inductively  from  the  examination 
of  special  cases.     Indeed,  many  arithmetical  truths  were  first 
discovered  in  this  way  and  afterward  demonstrated.     The  law 
tliat  "  every  number  is  a  triangular  number,  or  the  sum  of 
two  or  three  triangular  numbers  ;  a  quadrangular  number,  or 
tlie  sum  of  two,  tliree,  or  four  quadrangular  numbers;"  etc., 
has  never  lieen  demonstrated  except  for  triangular  and  square 
uuiubers,  though  it  is  known  from  induction  to  be  perfectly 
general. 

The  same  method  of  reasoning  is  possible  also  in  algebra. 
Newton's  Binomial  Theorem  was  derived  by  pure  induction; 
iJie  author  left  no  demonstration  of  it,  and  yet  it  was  regarded 
as  one  of  his  greatest  discoveries  and  was  engraved  upon  his 
tomb  in  Westminster  Abbey.  Legendre,  in  his  Theory  of 
Numbers,  gives  a  formula  for  finding  the  number  of  primes  up 
to  a  certain  limit,  which  has  never  been  fully  demonstrated. 

Care  must  be  exercised  in  the  use  of  induction  in  mathe- 
matics;  some  proi)Ositlons  derived  by  imluclioii  were  subse- 
quentl}'  found  to  be  untrue.  Fermat  stated  that  the  formula 
2n»-(- 1  is  always  a  prime  when  rn  is  taken  any  term  in  the  series 
1,  2,4,  8,  16,  etc.;  but  Euler  found  that  2^'+l  is  a  composite 
number.  Euler  made  a  similar  mistake  in  his  formula  for 
.csulving  the  equation  x^-\-Ay='B,  which  was  detected  by 
Lagrange.  Some  of  the  formulas  for  primes  illustrate  the 
same  point.  Thus,  ./r^  +  j;4-41  gives  primes  for  the  first /or/^ 
values  of  x  ;  .c^+.r -f  17,  for  the  first  seventeen  values;  and 
2jc"-4-29,  for  twenty-nine  of  its  first  values. 


TREATMENT    OF   ARITHMETIC.  339 

lY.  The  Treatment  of  Arithmetic. 

The  Science  of  Arithmetic  is  embraced  in  the  three  opera- 
tions,— Synthesis,  Analysis,  and  Comparison.  Synthesis  and 
Analysis  give  rise  to  two  classes  of  operations,  distinguished 
as  Primary  and  Secondary,  or  Fundamental  and  Derivative. 

I.  Fundamental  Operations. — The  Fundamental  Opera- 
tions include  Addition,  Subtraction,  Multiplication,  and  Di- 
vision. They  are  called  fundamental  because  they  lie  at  the 
basis  of  all  other  arithmetical  operations. 

Definitions. — Addition  is  the  process  of  finding  the  sum  of 
two  or  more  numbers.  Subtraction  is  the  process  of  finding 
the  difference  of  two  numbers.  Multiplication  is  the  pro- 
cess of  finding  the  product  of  two  numbers.  Division  is  the 
process  of  finding  the  quotient  of  two  numbers.  By  using 
the  terms  product  and  quotient  in  defiuing  multiplication  and 
division,  we  secure  a  happ}'  uniformity  in  the  four  definitions 
that  has  not  heretofore  existed. 

Cases. — Each  of  these  operations  embraces  two  general 
cases:  first,  to  find  the  results  independently  of  the  notation 
used  to  express  numbers;  second,  to  find  the  results  of  num- 
bers as  expressed  in  written  characters.  The  first  case  in 
each  is  a  process  of  pure  arithmetic,  independent  of  any 
notation ;  the  second  case  in  each  has  its  origin  in  the  Arabic 
system  of  notation. 

Treatment. — The  two  distinct  cases  require  distinct  meth- 
ods of  treatment.  In  the  former  case,  we  operate  on  the 
numbers  directly  as  wholes;  in  the  latter  case,  we  operate  upon 
them  by  parts.  The  first  method  is  independent  of  any  nota- 
tion ;  the  second  method  in  each  is  developed  by  means  of  the 
elementary  results  obtained  by  the  first  method. 

We  obtain  the  elementary  sums  by  intuition ;  we  obtain  the 
elementary  differences  by  intuition,  or  by  an  inference  from 
the  elementary  sums;  we  obtain  the  elementary  products  by 
addition;  we  obtain  the  elementary  quotients  by  successive 


840  METHODS   OF   TEACHINO. 

subtraction,  or  by  a  reversing  of  the  elementary  products. 
These  elementary  results  are  used  in  obtaining  the  results 
with  large  numbers  expressed  in  the  Arabic  system.  A  brief 
discussion  of  the  philosophy  of  the  methods  of  oi>eration  with 
the  Arabic  system  is  recommended. 

II.  Secondary  Operations. — The  Secondary  Operations  are 
Composition  and  Factoring,  Common  Divisor  nnd  Common 
Multiple,  Involution  and  Evolution.  Tlie  new  division,  called 
Composition,  seems  necessary  for  scientific  completeness,  that 
each  analytical  operation  may  have  its  corresponding  syn- 
thetical operation.  It  is  also  convenient  in  naming  certain 
operations  for  which  we  formerly  had  no  appropriate  term. 

Definitions. —  Composition  is  the  process  of  forming  com- 
posite numbers  out  of  the  factors.  Factoring  is  the  process 
of  finding  the  factors  of  composite  numbers.  A  common 
divisor  of  two  or  more  numbers  is  a  number  that  will  exactly 
divide  each  of  them.  A  common  multiple  of  two  or  more 
numbers  is  a  number  which  is  one  or  more  times  each  of  those 
numbers.  It  is  usually  defined  as  a  number  which  contains 
these  numbers,  but  this  does  not  include  the  idea  of  multiple. 

Treatment. — In  treating  these  subjects,  we  first  establish 
some  general  principles,  and  then  derive  the  methods  of  op- 
eration from  these  principles.  It  will  be  well  to  require  the 
student-teacher  to  show  the  method  of  development  of  each 
division,  and  to  point  out  the  philosophy  of  the  method  of 
treatment. 

III.  Common  Fractions. — Integers  originate  in  a  synthesis 
of  units,  fractions  in  a  division  of  the  unit.  A  fraction  in- 
volves three  things:  first,  a  division  of  the  unit;  second,  a 
comparison  of  the  part  with  the  unit;  third,  a  collection  and 
numbering  of  the  parts,  A  Fraction  is  thus  a  triune  product 
— a-  result  of  analysis,  comparison,  and  synthesis.  A  fraction 
may  also  arise  from  the  comparison  of  numbers. 

Definition. — A   Fraction  is  a  number  of  equal  parts  of  a 
unit.     This  seems  to  be  an  improvement  on  "one  or  more 


TREATMENT   OF   ARITHMETIC.  341 

equal  parts  of  a  unit."  Since  the  parts  of  a  unit  are  num- 
bered, these  ma}'  be  called  fractional  imits,  and  a  fraction 
may  be  defined  as  a  number  of  fractional  units.  Among 
many  of  the  incorrect  definitions,  we  mention, — "A  fraction 
is  a  part  of  a  unit ;"  "  A  fraction  is  an  expression  for  one  or 
more  of  the  equal  parts  of  a  unit;"  "  A  fraction  is  nothing 
more  nor  less  than  an  unexecuted  division." 

Cases. — The  cases  of  fx-actions  are  all  included  under  ^\n- 
thesis,  Analj'sis,  and  Comparison.  To  perform  the  synthetic 
and  analytic  processes,  we  need  to  change  fractions  from  one 
form  to  another;  hence  Reduction  enters  largely  into  the 
treatment  of  fractions.  The  comparison  of  fractions  gives 
us  several  cases  called  Relation  of  Fractions.  The  student- 
teacher  may  state  the  cases. 

Treatment. — There  are  two  methods  of  developing  com- 
mon fractions,  known  as  the  Inductive  and  Deductive  Meth- 
ods. By  the  Inductive  Method,  we  solve  each  case  by  analy- 
sis, and  derive  the  rules  by  inference  or  induction.  By  the 
Deductive  Method  we  first  establish  a  few  general  principles, 
and  then  derive  rules  of  operation  from  these  principles.  The 
Inductive  Method  is  simpler  for  3'oung  pupils;  the  Deductive 
is  more  satisfactory  for  older  pupils.  The  student-teacher 
may  illustrate  both  methods. 

Principles. — The  deductive  method  is  based  on  certain 
principles  which  express  the  law  of  multiplying  or  dividing 
the  terms  of  a  fraction.  These  principles  can  be  demonstrated 
either  by  the  principles  of  division  or  independently  as  frac- 
tions. The  latter  method  is  by  far  the  better.  There  should 
be  a  real  demonstration,  and  not  some  loose  statement  such 
as  we  often  find  in  arithmetics. 

lY.  Comparison. — We  have  not  room  to  indicate  the  treat- 
ment of  comparison,  but  refer  the  student  to  the  author's 
Philosophy  of  Arithmetic.  A  review  of  the  subjects  of  arith- 
metic, pointing  out  the  philosophy  of  its  methods  of  treat- 
ment, would  be  of  advantage  to  the  student-teacher. 


342  METHODS   OF  TEACHING. 

y.  The  Course  in  Arithmetic. 

Arithmetic,  for  the  purpose  of  instruction,  may  be  divided 
into  two  parts;  Mental  Arithmetic  and  Written  Arithmetic. 
In  Mental  Arithmetic  the  problems  are  solved  without  the 
aid  of  written  characters.  In  Written  Arithmetic  the  opera- 
tions are  performed  with  the  aid  of  written  characters. 

Oral  Arithmetic. — Many  educators  divide  the  course  into 
Oral  and  Written  Arithmetic;  and  at  first  thought  such  a 
division  seems  plausible  and  natural.  Language  is  of  two 
kinds,  oral  and  written  ;  when  we  solve  problems  without 
written  characters  it  is  naturally  called  oral  arithmetic;  when 
the  operations  are  performed  with  written  characters  it  is 
naturally  called  written  arithmetic.  Such  a  division  is,  how- 
ever, a  mistake,  and  results  from  a  superficial  view  of  the 
subject.  Written  Arithmetic  is  just  as  oral  when  recited  as 
Mental  Arithmetic ;  and  Mental  Arithmetic  is  no  more  oral 
when  not  recited  than  Written  Arithmetic.  Both  are  oral 
when  recited ;  neither  is  oral  when  not  recited. 

Intellectual  Arithmetic Nearly   all    authors  of  Mental 

Arithmetic  call  their  works  Intellectual  Arithmetic.  The 
term  Intellectual  is,  however,  objectionable,  as  it  does  not 
accord  with  popular  usage.  No  one  thinks  of  calling  a  "  men- 
tal solution"  an  "  intellectual  solution ;"  or  would  say,  "  he 
solved  it  intellectually,"  but  rather,  "  he  solved  it  mentally." 

Practical  Arithmetic. — Many  authors  call  their  works  on 
written  arithmetic,  Practical  Arithmetic.  This,  however,  is  a 
misnomer;  all  arithmetic  should  be  practical,  mental  arithme- 
tic as  well  as  written  arithmetic.  The  proper  term  is  ivritten, 
to  indicate  that  we  employ  written  characters.  The  term 
"  Practical"  may  do  very  well  as  a  "  trade  mark  "  but  it 
should  not  pretend  to  any  scientific  accuracy.  It  was  sug- 
gested by  Orontius  Fineus,  in  1535,  in  a  work  entitled  Arith- 
metica  Practica ;  and  first  used  by  Joseph  Chapman  in  1732 
in  a  work  entitled  "  Practical  Arithmetic  Compleat." 


TREATilEXT    OF    ARITHMETIC.  343 

True  Division The  natural  division   of  the   subject    is, 

therefore,  into  Mental  Arithmetic  and  Written  Arithmetic. 
There  are  several  considerations  in  favor  of  the  term  Mental. 
First,  it  is  in  accordance  with  the  popular  usage,  for  all  per- 
sons would  say  of  a  solution  without  the  aid  of  written  char- 
acters, "  he  solved  it  mentally,"  and  not  "  orally"  or  "  intellec- 
tually." Second,  the  distinction  is  philosophical.  Both  meth- 
ods of  solution  employ  the  mind,  and  one  employs  the  written 
characters  also,  and  it  is  appropriate  to  distinguish  the  two 
methods  by  this  distinguishing  characteristic,  calling  that 
which  employs  written  characters  Written  Arithmetic,  and 
the  other,  which  is  purely  mental.  Mental  Arithmetic.  One  is 
purely  mental  and  the  other  mental  and  wj-itten,  a.nd  it  is  nat- 
ural and  convenient  to  distinguish  them  b}' names  which  indi- 
cate these  distiuguishinir  characieristics. 

School  Course. — The  common  school  course  of  arithmetic 
may  be  divided  into  two  parts ;  Primary  Arithmetic  and  Ad- 
vanced Arithmetic.  The  Primary  Arithmetic  is  designed  to 
teach  a  child  the  elementar}^  ideas  and  processes  of  arithmetic; 
the  Advanced  Arithmetic  is  designed  to  present  as  full  a 
knowledge  of  the  science  as  should  be  taught  in  our  public 
schools.  In  some  schools  a  course  in  Higher  Arithmetic  may 
also  be  required,  including  the  more  abstruse  principles  of  the 
science  and  a  more  extended  application  of  them. 

2f  umber  of  Books. — If  mental  and  written  exercises  are 
combined  after  the  Primar}-  Arithmetic,  the  entire  course  may 
be  embraced  in  two  books,  which  ma}-  be  called  the  Primary 
Arithmetic  and  the  Union  Arithmetic.  If  it  is  thought  best 
to  separate  the  mental  and  written  exercises  after  the  first 
book,  we  shall  have  three  books  in  the  course,  which  may  be 
distinguished  as  the  Primary  Arithmetic,  Mental  Arithmetic, 
and  Written  Arithmetic.  In  schools  of  a  certain  grade  there 
has  been  a  demand  for  a  book  between  Primary  and  Advanced 
Arithmetic,  svhich  has  been  met  by  an  Elementary  Arithmetic. 
Union  Arithmetic. — Mental  and  written  exercises  should 


344  METHODS   OF   TEACHING. 

be  combined  in  the  Primary  Arithmetic,  and  many  teachers 
advocate  this  union  throiijjliout  the  entire  course.  The  reasons 
are:  1.  Economy  of  time;  2.  Econom}'  in  the  purchase  of 
books;  3.  One  aids  in  learning  the  other  ;  4.  The  sole  object  of 
Mental  is  to  aid  in  the  study  of  Written.    The  objections  are  ; 

1.  Their  object  is  different ;  the  object  of  Mental  is  discipline 
in  analysis,  the   object   of  Written   is  skill  in    calculation ; 

2.  Their  spirit  is  diverse  ;  one  being  analytic  and  the  other 
more  synthetic ;  3.  They  cannot  be  properly  coordinated ; 
4.  Hence  to  combine  is  to  neglect  Mental.  The  present  desire 
for  combination  is  an  example  of  history  repeating  itself,  as 
may  be  seen  in  the  works  of  Smith,  Emerson,  etc.  Whether 
this  demand  will  be  permanent,  or,  like  a  new  fashion,  change 
again  in  a  few  years,  time  will  decide. 

Ejctent  of  Course. — Many  teachers  think  the  present  com- 
mon school  course  in  arithmetic  too  extensive,  but  we  doubt  it. 
The  child  needs  a  thorough  drill  in  arithmetic  for  the  thought- 
power  it  imparts;  and  for  the  practical  value  of  arithmetical 
knowledore.  Every  child  coming  out  of  our  public  schools 
should  have  a  good  practical  knowledge  of  nearly  every  sub- 
ject treated  in  the  ordinary  common  school  arithmetic  to 
prepare  him  for  the  practical  duties  of  the  business  world. 

Course  in  Arithmetic. — We  shall  discuss  the  subject 
under  three  heads;  Primary  Arithmetic,  Mental  Arithmetic, 
and  Written  Arithmetic.  These  three  parts  are  not  entirely 
distinct ;  to  some  extent  they  run  into  and  overlap  one  an- 
other; but  a  clearer  idea  of  the  principles  and  methods  of 
instruction  can  be  given  by  such  a  division.  The  several  sul> 
jects  embraced  in  the  course  are  as  follows  : — 1.  Ideas  of 
Numbers;  2.  Arithmetical  Language  ;  3.  Operations  of  Arith- 
metic ;  4.  Reasoning  of  Arithmetic ;  5.  Definitions  of  Arith- 
metic ;  6.  Rules  of  Arithmetic  ;  7.  Principles  of  Arithmetic  ; 
8.  Applications  of  Arithmetic.  In  the  next  three  chapters  we 
shall  consider  the  methods  of  teaching  Arithmetic. 


CHAPTER  III. 

TEACHING   PRIMARY   ARITHMETIC. 

niHE  course  in  Primaiy  Arithmetic  should  embrace  the 
X  Ideas  of  Numbers,  Arithmetical  Language,  the  Funda- 
mental Operations  of  Synthesis  and  Anah'sis,  the  Elements 
of  Fractions,  and  the  Elements  of  Denominate  Numbers.  In 
other  words,  the  course  should  embrace  the  elements  of 
Numeration  and  Notation,  the  elements  of  Addition,  Subtrac- 
traction,  Multiplication,  and  Division,  the  elements  of  Frac- 
tions, and  the  elements  of  Denominate  Numbers. 

Principles  of  Teachivff. — In  presenting  these  subjects  to 
the  learner,  it  is  believed  that  the  course  of  instruction  should 
be  based  upon  the  following  principles : 

1.  The  first  lessons  in  arithmetic  should  be  given  by  means 
of  oral  exercises.  Such  instruction  is  needed  for  several 
reasons:  First,  pupils  can  learn  arithmetic  before  they  can 
read;  and  hence,  of  course,  before  they  can  use  a  book. 
Second,  even  with  pupils  who  can  read,  such  exercises  are 
a  very  valuable  preparation  to  the  study  of  the  subject  in  the 
text-book.  Third,  more  thought  can  be  developed,  more  in- 
terest awakened,  and  much  more  i-apid  and  thorough  progress 
can  be  made  with  such  exercises.  These  exercises  should  be 
continued  thi-oughout  the  entire  course  in  arithmetic.  Every 
subject,  even  in  the  more  advanced  parts  of  written  arith- 
metic, should  be  introduced  b}^  such  exercises. 

2.  The  first  lessons  in  Primary  Arithmetic  should  be  given 
by  means  of  sensible  objects.  Such  exercises  will  give  distinct 
ideas  of  arithmetical  quantities.  Children's  numerical  ideas 
are  often  vague  and  indefinite.  The  names  of  numbers  are 
often  merely  abstract  terms  to  them.  The  denominations 
ounces,  gills,  pints,  cords,  etc.,  are  often  mere  words  without 

15*  (545) 


346  METHODS   OF   TEACHING. 

any  concrete  meaning  to  them.  The  ideas  and  processes  of 
fractions  cannot  be  clearl}'  understood  by  children  without 
such  illustrations. 

The  objects  used  ma}'  be  marbles,  grains  of  com,  beans, 
peas,  little  blocks,  etc.  Dr.  Hill  says  the  whole  science  of 
arithmetic  may  be  taught  with  a  pint  of  beans.  The  most 
convenient  object  for  man}'  of  the  processes  is  the  Numeral 
Frame,  or  Abacus.  This  should  be  in  every  public  school, 
and  should  be  in  constant  use.  Large  ones,  three  or  four  feet 
square,  are  used  in  the  primary  schools  of  Sweden,  Germany, 
etc.  Mauy  authors  give  pictures  of  objects,  marks,  stars, 
etc.,  in  their  books;  but  these  do  not  seem  to  be  necessary, 
as  the  objects  themselves  are  better  than  the  pictures  of 
objects.  Besides,  no  pupil  should  begin  to  study  arithmetic 
in  a  text -book,  who  needs  pictures  to  aid  in  the  primary 
operations. 

3.  In  Primary  Arithmetic^  the  order  of  instruction  is, — 
first  the  method,  then  the  reason  for  it;  first  the  mechanical 
part,  then  the  rational.  This  is  the  natural  order  of  develop- 
ment with  children;  fin^t  the  hoio  and  then  the  why.  Methods 
of  doing  should  be  taught  before  the  reasons  for  doing;  ideas 
should  be  taught  before  the  expression  of  them;  operations 
before  rules  describing  operations.  Principles  should  follow 
problems;  not  precede  them.  Much  precious  time  has  been 
wasted  in  primary  instruction  hy  the  violation  of  this  prin- 
ciple; and  minds  have  been  dwarfed  by  being  led  to  incorrect 
habits  of  study  and  thought. 

4.  In  Primary  Arithmetic,  the  method  of  teaching  should 
be  inductive.  The  pupil  should  be  led  to  each  new  idea  and 
process  by  appropriate  questions  and  illustrations.  The  defi- 
nition should  be  drawn  from  the  ideas,  rather  than  the  ideas 
from  the  definition.  The  pupil  should  be  led  to  see  the  prin- 
ciple clearly  before  he  is  required  to  state  .it ;  and  rules  or 
methods  should  be  derived  b}'  inductive  inferences  from 
analytic  solutions.     The  child  should  be  led  to  see  the  propri- 


TEACHING    PRIMARY   ARITHMETIC.  347 

ety  of  a  new  term  for  the  expression  of  a  new  idea,  when  pos- 
sible, for  he  will  then  see  the  meaning  of  it. 

5.  Mental  and  Written  Arithmetic  should  be  united  in  Pri- 
mary Arithmetic.  This  is  indicated  by  the  logical  relation  of 
the  subjects.  As  soon  as  the  pupil  can  express  arithmetical 
ideas  oralh",  he  is  ready  to  learn  to  express  them  in  written 
lan2:ua<Te.  This  comliination  is  also  a  matter  of  practical  con- 
venience. A  pupil  will  learn  more  rapidly  b}*  having  the  two 
taught  together.  Each  will  throw  light  upon  the  other,  and 
assist  the  pui)il  in  understanding  and  remembering  it.  Men- 
tal and  written  exercises  are  mutually  dependent  in  the  pri- 
mary processes;  the  mental  exercise  prepares  for  the  writ- 
ten, and  the  written  aids  the  mental.  They  should,  therefore, 
go  hand  in  hand  in  primary-  instruction. 

Whether  these  exercises  should  be  mixed  along  through  the 
book,  or  whether  they  should  be  given  separately,  requiring 
the  teacher  to  mix  them  in  his  instruction,  is  a  question.  As 
an  abstract  question,  we  believe  it  would  be  best  to  give  them 
separately  and  have  the  teacher  combine  them  in  his  instruc- 
tion. With  young  and  inexperienced  teachers,  however,  it 
will  probably  be  best  for  the  text-book  to  unite  the  two  kinds 
of  exercises  as  the  author  thinks  they  should  be  naturally 
developed  together. 

I.  Teaching  Arithmetical  Ideas  and  Language. 

Aeithmetical  Ideas. — The  first  step  in  the  science  of  num- 
bers is  the  attainment  of  numerical  ideas.  The  ideas  of  num- 
bers originate  in  a  succession  of  mental  states  constituting 
periods  of  time.  With  children  the  idea  begins  with  the 
perception  of  objects,  and  is  developed  by  a  process  called 
counting.  The  earliest  ideas  are  usually  learned  upon  the 
mother's  knee,  as  she  fondles  with  the  little  fingers,  or  num- 
bers the  toys  with  which  childhood  beguiles  the  happy  hours. 
Still,  though  a  child  may  be  able  to  count  when  entering 
school,  an  exercise  for  a  fuller  development  of  the  numerical 
idea  should  not  be  omitted. 


348  METHODS   OF   TEACHING. 

Ill  counting,  we  should  not  rest  satisfied  with  the  mere 
namins;  of  numbers  in  succession,  for  a  child  may  do  this  and 
have  no  idea  of  the  meaning  of  the  words  used.  One,  two, 
three,  etc.,  may  be  to  it  a  mere  succession  of  sounds,  like  do, 
re,  mi,  etc.,  without  embodj'ing  any  idea  of  collections.  Chil- 
dren have  been  known  to  run  off  these  words  very  glibly,  even 
as  far  as  a  hundred,  without  being  able  to  select  a  dozen 
grains  of  corn  from  a  collection. 

ChiUren  should  be  required  to  count  with  objects.  The 
numeral  frame  is  the  most  convenient,  though  other  objects 
may  be  used.  A  counting  exercise  may  be  made  lively  by  in- 
creasing and  diminishing  the  number  by  several  at  the  same 
time.  Little  counting  games  with  beans  or  grains  of  corn, 
will  also  be  found  interesting.  Counting  exercises  should  be 
continued  until  the  pupils  can  count  readil}^  and  have  definite 
ideas  of  numbers.  If  pupils  can  count  when  the}-  enter  school, 
these  exercises  need  not  be  continued  long.  Pupils  should  be 
taught  to  count  backwards  as  well  as  forwards.  This  will  be 
of  advantage  in  learning  to  subtract,  as  we  may  "  count  off" 
to  find  a  difference,  as  well  as  "count  on"  for  a  sum. 

Arithmetical  Language. — Arithmetical  Language  is  the 
method  by  which  we  express  numbers.  It  is  both  oral  and 
written;  the  former  is  called  Numeration,  the  latter  is  called 
Notation.  In  teaching  arithmetical  language,  Numeration 
should  precede  Notation.  This  appears  from  the  fact  that  oral 
language  comes  before  written  language.  This  is  a  point  which 
seems  to  have  been  overlooked  by  some  writers,  for  they  speak 
of  "  Notation  and  Numeration,"  as  if  the  latter  followed  the 
former  in  the  natural  order.  The  reason  for  this  mistake  is 
that  ihey  restrict  Numeration  to  the  reading  of  numbers  after 
the}'  are  expressed  in  figures. 

Numeration. — The  oral  language  of  arithmetic  must  be 
taught  in  connection  with  the  development  of  the  idea  of 
number.  The  idea  and  the  word  are  so  intimately  related 
that  the  former  leads  immediately  to  the  latter;  they  are  twin- 


TEACHING   PRIMARY   ARITHMETIC.  349 

born,  and  go  hand  in  hand  in  pure  arithmetic.  The  names  of 
numbers  are,  therefore,  taught  with  objects  and  bj'  means  of 
counting. 

Two  Methods. — There  are  two  methods  of  teaching  the 
names  of  numbers,  which  may  be  distinguished  as  the  Com- 
mon Method  and  the  Scientific  Method.  These  two  methods 
agree  as  far  as  ten.  By  the  Common  Method,  we  teach  chil- 
dren to  say  eleven^  twelve^  thirteen^  etc.,  using  the  names  after 
ten  just  as  arbitrarily  as  we  do  the  names  of  the  first  simple 
numbers  up  to  ten.  The  method  does  not  indicate  to  the 
pupil  the  method  by  which  numbers  are  named, — that  is,  the 
principle  of  grouping  by  tens. 

By  the  Scientific  Method,  when  we  reach  ten^  we  give  the 
pupils  the  idea  of  a  group,  and  then,  instead  of  having  them 
say  eleven^  ttvelve,  etc.,  we  require  them  to  say  one  and  ten,  two 
and  ten,  three  and  ten,  etc.,  up  to  ten  and  ten,  which  we  show 
them  consists  o^two  groups  often,  and  teach  them  to  count  two 
tens,  two  tens  and  one,  etc.,  etc.  After  the  pupils  are  familiar 
with  these  forms,  we  show  them  that  these  expressions  have 
been  changed  into  those  in  common  use;  thus,  three  and  ten 
may  be  abbreviated  by  dropping  the  "and,"  changing //iree  to 
thir,  and  ten  to  teen,  giving  thirteen ;  and  similarly  for  the 
other  names. 

The  advantage  of  this  method  of  teaching  the  names  of 
numbers  is,  that  it  leads  pupils  to  see  the  principle  by  which 
numbers  are  named  which,  by  the  ordinary  method,  is  so  con- 
cealed that  it  generally  never  occurs  to  their  minds.  It  is 
also  an  excellent  preparation  for  Notation,  and  greatly  sim- 
plifies the  task  of  teaching  pupils  to  express  numbers  by 
figures.  Some  excellent  teachers  of  primary  arithmetic  teach 
pupils  to  count  by  using  one-teen,  two-teen,  three-teen,  etc., 
also  two-ty  one,  two-ty  two,  etc.,  that  they  may  see  the  law  bv 
which  numbers  are  named. 

The  groups  may  be  indicated  by  the  numeral  frame,  or  by 
a  little  bundle  of  sticka ,  or  by  marks  on  the  board  enclosed 


350  METHODS   OF   TEACHING. 

by  a  circle.  The  grouping  of  ten  tens  for  the  hundred,  and 
(en  hundreds  for  the  thousand,  may  also  be  explained  and 
illustrated.  The  law  of  naming  numbers  beyond  the  thou- 
sand is  best  illustrated  in  connection  with  the  writino-  of 
numbers. 

Notation. — When  the  pupils  have  acquired  a  little  famil- 
iarity with  the  oral  language  of  arithmetic,  they  are  to  be 
taught  its  written  language.  As  soon  as  the}'  have  learned  a 
few  names  of  numbers,  the}'  should  learn  to  express  them  in 
written  characters.  A  knowledo^e  of  the  written  lan^ua^e  of 
arithmetic  includes  a  knowledge  of  the  characters  and  the 
method  of  combining  them.  We  first  teach  the  arithmetical 
characters  to  express  the  first  few  numbers,  and  then  their 
combination  to  express  the  numbers  above  nine. 

The  Characters. — We  first  give  the  nine  digits,  and  drill 
the  children  in  naming  and  writing  them  until  they  are 
entirely'  familiar  with  these  characters.  If  they  have  learned 
a  little  addition  and  subtraction,  they  may  use  the  characters 
in  solving  simple  problems,  the  teacher  giving  no  problem  at 
present  which  involves  a  number  greater  than  nine.  Before 
the  teacher  explains  the  method  of  expressing  numbers  be- 
yond nine,  it  would  be  well  to  have  the  pupils  try  how  the}- 
would  express  twelve,  thirteen,  etc.,  with  the  characters  which 
they  have  learned.  Their  ver}'  failure  will  prepare  them  tr 
appreciate  the  correct  method  when  presented  by  the  teacher. 

Combination  of  Characters. — There  are  two  methods  of 
teaching  the  combinations  of  the  characters,  or  of  teaching 
the  written  language  from  one  to  one  hundred,  which  may  be 
distinguished  as  the  Common  Method  and  the  Scientific 
Method.  By  the  Common  Method,  we  give  the  combined 
characters  without  explaining  the  principle  of  the  combina- 
tion. Thus  we  teach  that  10  expresses  ten,  11  expresses 
eleven,  12,  twelve,  etc.,  without  an}'  reference  to  tens  and  units. 
This  is  the  method  which  is  usually  employed,  and  seems  to 
be  preferred  to  the  scientific  method. 


TEACHING    PRIMARY    ARITHMETIC.  351 

By  this  method,  we  would  give  the  expressions  for  numbers 
as  far  as  20,  and  then  drill  the  pupils  in  reading  and  writing 
them  until  the}''  were  entirely  familiar  with  them.  We  wouhl 
next  give  the  expressions  from  20  to  30,  and  drill  in  like  man- 
ner and  thus  continue  as  far  as  100.  After  pupils  are  familiar 
with  this  method  of  writing  numbers  as  far  as  100,  the  teacher 
may  show  the  pupils  the  principle  of  the  combination,  that 
the  figure  in  the  first  place  represents  ones  or  units,  in  the 
second  place  tens,  etc.  When  this  is  understood,  we  should 
require  the  class  to  analyze  these  expressions  as  follows : 
Analyze  25  (twenty-five).  In  25,  the  5  represents  5  units, 
and  the  2  represents  2  tens. 

By  the  Scientific  Method  we  explain  the  principle  of  the 
combination  at  the  beginning.  Having  taught  the  pupils  to 
count  one  and  ten,  two  and  ten,  etc.,  we  tell  them  that  1  placed 
at  the  left  of  another  figure  expresses  a  teii,  and  thus  that  14 
expresses  4  units  and  1  ten,  or  '''four  and  ten;^'  that  13  ex- 
presses 3  and  1  ten,  or  '■'•three  and  ten,''''  etc.  Finall}-,  the}' 
may  be  led  to  see  that  since  1  ten  is  expressed  by  a  1  in  the 
second  place,  we  need  a  character  to  express  no  ones  in  the 
first  place.  We  then  tell  them  that  we  use  the  zei-o,  0,  for 
this  purpose,  and  thus  represent  ten  by  10,  which  is  1  ten  and 
0  ones. 

The  latter  of  these  two  methods  is  preferable.  It  is  more 
philosophical,  for  it  shows  the  principle  of  the  Arabic  method 
from  the  beginning,  which  the  common  method  conceals.  It 
is  more  practical,  for  pupils  will  learn  to  write  numbers  much 
more  readily  by  it  than  by  the  other  method.  Give  the  pupils 
a  few  examples  to  illustrate  the  principle,  and  they  will  be 
able  to  express  the  rest  of  the  numbers  up  to  99  without  be- 
ing shown  by  the  teacher.  Moreover,  perceiving  the  princi- 
ple of  place  value  in  the  small  numbers,  they  will  have  no 
difficulty  in  understanding  it  when  applied  to  hundreds,  thou- 
w.nds,  etc. 

Higher  Groups. — After  pupils  are  familiar  with  the  naming 


352  METHODS   OF   TEACHING, 

and  writing  of  numbers  up  to  ninety-nine,  they  should  be 
taught  that  the  next  group  consists  of  ten  tens,  and  is  called  a 
hundred,  and  that  the  hundreds  are  expressed  b}'  a  figure  in 
the  third  place.  They  should  then  be  drilled  until  they  can 
read  and  write  in  units,  tens,  and  hundreds.  They  should 
then  be  taught  that  a  group  of  ten  hundreds  is  called  a  thou- 
Hind,  that  thousands  are  expressed  by  a  figure  in  the  fourth 
I  luce. 

They  should  then  be  shown  that  the  law  of  giving  a  new 
name  for  each  higher  group  of  tens  is  chan2;ed  to  giving  anew 
name  for  each  third  group ;  and  that  the  intermediate  names 
and  places  are  tens  and  hundreds  of  the  old  group.  Up  to 
this  time  the  numeration  has  preceded  and  led  the  notation 
in  the  order  of  teaching  ;  after  this  it  will  be  more  convenient 
to  invert  the  order,  and  let  the  notation  lead  the  numeration. 
Numeration  will  thus  be  regarded  not  only  as  a  method  of 
naming  numbers,  but  of  reading  them  when  they  are  writ- 
ten in  Arabic  charactei's. 

Numerical  Periods. — The  pupils  may  then  be  taught  to 
separate  written  numbers  into  numerical  periods,  and  to 
name  and  remember  the  periods.  Perpendicular 
lines  may  be  drawn,  and  the  columns  headed 
units,  tens,  etc.,  and  the  pupil  be  drilled  in  writ- 
ing numbers  b}'  putting  the  terms  in  the  proper 
column.  Such  an  exercise  is  not  of  much  value 
if  the  teacher  knows  how  to  teach  by  the  method  previously 
suggested.  The  pupils  should  be  drilled  in  reading  and  writ- 
ing numbers  until  the}'  are  entirely  familiar  with  the  subject. 
Do  not  hurry  over  the  subject;  haste  here  is  "bad  speed."  A 
thorouijh  knowledsre  of  Numeration  and  Notation  will  remove 
the  usual  difficulties  of  the  fundamental  rules. 

This  instruction  in  reading  and  writina;  the  larg-er  numbers 
should  be  presented  gradually,  in  connection  with  the  exer- 
cises in  the  fundamental  rules.  Do  not  keep  the  pupil  at  it 
until  he  has  mastered  it,  but  go  on  with  adding  and  subtract- 


H. 

T. 

u 

3 

5 

T 

6 

3 

8 

5 

0 

6 

TEACHING    PRIMARY    ARITHMETIC.  353 

ing,  etc.,  returning  to  the  notation  and  numeration  every  day, 
thus  keeping  up  a  constant  review,  and  adding  a  little  to  what 
has  been  previously  given,  as  the  pupils  are  ready  for  it.  The 
student-teacher  will  now  give  a  model  lesson  in  teaching 
arithmetical  language. 

II.  Teaching  Addition  and  Subtraction. 

While  pupils  are  obtaining  the  ideas  and  names  of  numbers, 
and  learning  to  read  and  urite  them,  they  should  begin  to  unite 
and  separate  them ;  that  is,  they  should  begin  the  processes  of 
Addition  and  Subtraction. 

Principles  of  Teaching. — Instruction  in  these  processes 
should  bo  given  in  accordance  with  the  following  principles: 

1.  Addition  and  Hiibtrartion  should  be  taught  simultan- 
eoudy.  This  is  indicated  by  the  logical  relation  of  the  sub- 
ject. Subtraction  is  the  converse  of  addition,  and  the 
elementary  differences  should  be  derived  from  the  elementary 
sums.  Thus,  as  soon  as  the  child  sees  that  3  and  2  are  5,  he 
is  ready  to  see  that  5  less  2  is  3,  or  5  less  3  is  2.  Thus,  also, 
in  finding  the  difference  of  9  and  5,  instead  of  counting  5  oflf 
from  9  to  see  what  remains,  he  should  infer  the  difference  by 
knowing  that  4  and  5  are  9.  The  synthesis  of  numbers  in 
obtaining  the  sum  should,  therefore,  be  accompanied  by  the 
analysis  of  numbers  in  finding  the  difference. 

This  method  will  be  found  to  be  especially  convenient  in 
practice.  Taught  in  this  way,  the  pupil  will  learn  the  ele- 
mentary differences  while  he  is  learning  the  elementary  sums. 
He  will  thus  not  need  to  commit  a  Subtraction  Table,  which 
seems  almost  a  necessity  if  subtraction  is  taught  separately 
from  addition.  Knowing  the  elementary  suras,  if  he  has  been 
tauoht  to  derive  the  differences  from  the  sums,  he  can  imme- 
diately obtain  a  difference  without  resorting  to  a  table. 

2.  Addition  and  Subtraction  should  be  taught  by  means  of 
sensible  objects.  This  is  indicated  by  the  nature  of  the  sub- 
ject aiid  iLt  mind      h  is  ihe  way  in  which  the  jjupils  really 


354  METHODS   OF   TEACHING. 

must  attain  the  sums  of  numbers,  if  tlie}^  are  to  understand 
them.  So  strong  is  this  necessity  that,  if  the  teacher  does 
not  require  pupils  to  use  objects,  they  -will  themselves  use 
them  by  counting  their  fingers  or  using  marks  on  the  slate  or 
blackboard.  What  the  pupils  do  by  nature,  the  teacher 
should  require  to  be  done  upon  principle.  They  should  be 
required  to  see  the  sums  before  they  say  them.  The  most 
convenient  object  for  this  purpose  is  the  numeral  frame. 

The  teacher  should  be  careful,  however,  not  to  allow  the 
pupils  to  use  objects  too  long  in  adding  and  subtracting. 
They  should  be  led  from  the  concrete  to  the  abstract,  from 
seeing  sums  and  ditferences,  to  thinking  them.  The  habit,  in 
pupils  of  nine  or  ten  years  of  age,  of  counting  the  fingers  or 
using  strokes,  shows  poor  teaching;  and  the  practice  should 
not  be  allowed. 

3.  Pupils  should  be  required  to  commit  an  addition  table. 
The  neglect  of  this  is  very  common,  and  the  result  is  that 
ver}^  few  pupils  are  ready  in  adding.  It  is  not  an  unusual 
thing  to  see  pupils  who  are  entirely  familiar  with  the  multi- 
plication table,  using  strokes  or  counting  their  fingers  in  solv- 
ing simple  problems  in  addition  and  subtraction.  There  is 
the  same  reason  for  committing  an  addition  table  as  there  is 
for  committing  a  multiplication  table.  Pupils  should  be  re- 
quired to  make  and  study  an  addition  table.  They  should 
write  it  on  the  board,  that  seeing  it  may  aid  to  fix  it  in  the 
memory. 

Course  of  Lessons. — The  course  of  lessons  in  Mental  Addi- 
tion and  Subtraction  is  as  follows: 

1.  Teach  the  pupil  to  increase  and  diminish  by  ones  as  far  as  12  and  1, 
or  13. 

2.  Teach  the  pupil  to  increase  and  diminish  by  twos  as  far  as  12  and  2, 
or  14. 

3.  Teach  the  pupils  to  increase  and  diminish  by  threes  as  far  as  12  and 
8,  or  15. 

4.  Teach  the  pupils  to  increase  B.ndt.  diminish  hj  fours,  hy fives,  by  sixes, 
etc.,  up  to  12  and  12,  or  24. 


TEACHING    PRIMARY    ARITHMETIC,  S56 

9 

5.  Have  the  pupils  write  these  sums  and  differences  in  a  talle  and 
fludy  and  recite  tliem. 

6.  Teach  them  to  increase  a  number  greater  tlian  12  by  1,  2,  3,  etc. 
Thus,  since  14  and  5  are  19,  24  and  5  are  29,  etc.  Also  to  diminish  in 
a  similar  manner. 

Model  Lesson. — Teacher,  taking  one  l)ook  in  his  hand,  asks.  How  many 
books  have  I  in  my  hand?  Pupils.  One  book.  Teacher,  taking  another 
book  in  his  hand,  asks,  How  m;iny  books  have  I  now  ?  P.  Two  books. 
T.  Row  many  then  are  one  book  and  one  book  ?  P.  Two  books.  T. 
How  many  then  are  one  and  one  ?  P.  One  and  one  are  two.  T.  How 
many  books  have  I  in  my  hand  ?  P.  Two  books.  T.  I  will  take  one 
book  away;  how  many  books  have  I  now?  P.  One  book.  T.  One  book 
taken  from  two  books  leaves  how  many  books?  P.  One  book.  T.  One 
from  two  leaves  how  many  ?  P.  One  from  two  leaves  one.  Continue 
this  exercise,  and  apply  it  also  to  tico,  three,  etc. 

Practical  Exercises. — The  following  exercises  will  be 
found  valuable  in  teaching  pupils  to  add  and  subtract  with 
readiness  and  accuracy.  Frequent  drill  upon  such  exercises 
is  recommended. 

First  Exercise. — The  teacher  will  name  two  numbers  and  require  the 
pupils  to  give  first  their  sum,  and  then  their  difference;  thus,  the  teacher 
says,  "5  and  2?"  Pupils.  "5  and  2  are  7,  and  2  from  5  leaves  3."  After 
a  little  practice  they  may  omit  naming  the  numbers,  and  merely  say,  "The 
sum  is  7,  the  difference  is  3;"  or  "7,  3."  To  vary  this,  the  boys  may  give 
the  sum,  and  the  girls  the  difference,  and  vice  versa;  or,  if  the  class  is 
all  of  one  sex,  a  division  may  be  made,  one  part  giving  the  sum,  and  the 
other  the  difference.  In  this  and  the  following  exercises,  care  should  be 
taken  that  small  numbers  be  used  at  first,  until  the  pupils  attain  the 
ability  to  use  larger  numbers  with  ease  and  readiness. 

Second  Exercise. — The  teacher  will  select  some  number,  and  then  give 
one  part  of  this  number  and  require  the  pupils  to  give  the  other  part. 
Suppose  8  to  be  the  number;  the  teacher  says  "J?ee,"  pupils  answer, 
"three;"  teacher,  "two,"  pupils,  "sir,"  etc.,  etc. 

Third  Exercise. — The  pupils  should  also  be  required  to  add  by  twos, 
threes,  etc.,  merely  naming  the  results,  as  follows  :  2,  4,  6,  8,  etc.,  3,  6,  9, 
etc.,  until  the  additions  can  be  readily  given.  Begin  also  with  one,  and 
comit  by  twos,  thus  :  1,  3,  5,  7,  etc.;  also  at  1,  and  count  by  threes,  thus: 
1,  4,  7,  10,  etc.;  also  at  2,  thus:  2,  5,  8,  11,  etc.;  continuing  the  addition 
au  far  as  it  may  be  thought  desirable. 

Let  the  pupil  in  a  similar  manner  add  ])y  fours,  fives,  "tc,  uptotweloes. 


1 

1 

2 

2 

3 

3 

4 

4 

5 

5 

6 

6 

7 

7 

8 

8 

9 

9 

3">6         ,  METHODS   OF   TEACHING. 

Such  exercises  should  be  continued  day  after  day,  in  connection  witb 
the  lessons  which  precede  and  follow  this  lesson,  until  great  facility  ia 
acquired  in  the  operations. 

Fourth  E.cercise. — Give  a  pupil  a  number  and  require  him  to  separate 
it  into  two  parts;  then  inio  three  parts,  etc.  Thus  6=34-3  ;  6^4-)-2; 
6=5+1.     Also  6=2+2-h3;  6=4+1  +  1;  6=3+1+2  ;  etc. 

Fifth  Exercise. — Let  the  teacher  write  two  columns  of  figures  on 
the  board,  as  indicated  in  the  margin.  Call  the  firet  column 
additive,  and  the  second  subtractive.  The  teacher  then  with  the  +  — 
pointer  will  indicate  the  number,  the  operation  being  indi- 
cated by  the  column.  When  he  points  to  a  figure  in  the  first 
column,  the  number  which  it  indicates  will  be  added,  but  when 
he  points  to  a  figure  in  the  second,  the  number  indicated  will 
be  subtracted  from  the  result  which  the  pupils  have  pre- 
viously obtained.  If  the  Arabic  characters  have  not  been 
given,  numerical  words  may  be  written  in  columns,  instead  of 
the  figures. 

These  exercises  may  be  conducted  sometimes  in  concert  and  sometimes 
singly.  While  one  is  adding  alone,  let  the  others  keep  careful  watch  for 
errors  ;  a  good  degree  of  interest  may  thus  be  created,  each  pupil  trying 
to  obtain  the  largest  sum  before  making  a  mistake. 

Written  Addition. — While  the  pupils  are  learning  to  add 
and  subtract  mentally,  they  should  also  perform  work  on  the 
slate  and  blackboard  with  written  characters.  These  exer- 
cises should  first  extend  as  far  as  the  elementary  sums,  that 
is,  to  about  "  12  and  12  are  24."  So  far  written  addition  and 
subtraction  should  go  together  with  the  mental  exercises  ;  but 
subsequently  it  is  more  convenient  to  separate  them,  teaching 
first  addition  and  then  subtraction. 

Cases. — Written  Addition  should  be  presented  in  two  cases ; 
first,  where  there  is  nothing  "  to  carry ;"  and  second,  where 
there  is  something  to  carry.  In  both  cases,  we  should  first 
require  the  pupils  to  learn  to  perform  the  operation  without 
giving  an}-  reason  for  it.  The  primaiy  object  is  to  make  them 
familiar  with  the  mechanical  operations.  Subsequently  they 
may  learn  to  explaiu  ihe  woik 

Course  of  Liessons, — The  course  ol  lesaonb  iii  W  niiti. 
Addition  is  as  follows  ; 


TEACHING   PRIMARY    ARITHMETIC.  357 

1.  To  write  the  elementary  sums  of  the  addition  table. 

2.  To  add  single  columns  of  numbers,  in  which  the  sum  exceeds  nine. 

3.  To  add  numbers  of  two,  three,  four,  etc.,  terms,  in  which  there  la 
nothing  to  carry. 

4.  To  add  two  columns  in  which  there  is  something  to  carry,  then 
three  columns,  etc. 

Explanation. — The  explanation  may  be  given  in  what  is 
called  the  Simple  Foi"m  or  in  what  is  called  the  Full  Form. 
B}'  the  Simple  Form,  the  pupil  will  merely  state  the  method 
without  giving  the  reason  for  it.  By  the  Full  or  Complete 
Form,  the  puj^il  gives  the  logical  solution,  which  states  each 
step  in  the  process  and  the  reason  thereof.  Young  pupils 
should  use  the  simple  form,  as  they  are  not  prepared  to 
understand  and  state  the  reasons  for  the  various  operations. 
Much  time  has  been  wasted,  and  man}-  j-outhful  minds  injured, 
by  the  attempt  to  have  children  give  logical  forms  of  explana- 
tion before  they  were  prepared  for  them.  With  more  ad- 
vanced pupils,  we  should  require  full  explanations,  in  concise, 
simple,  and  logical  language,  showing  the  reason  for  every 
step  of  the  process.  For  the  two  forms,  see  the  author's 
Primary  and  Elementary  Arithmetics.  The  student-teacher 
will  illustrate  the  subject  in  model  lessons. 

Written  Subtraction. — After  the  pupil  is  somewhat 
familiar  with  Written  Addition,  he  should  begin  Written 
Subtraction.  The  subject  should  be  presented  under  two 
cases:  1st,  To  subtract  without  "borrowing;"  2d,  To  sub- 
ti'act  by  "borrowing."  The  first  of  these  cases  should  be 
taught  before  the  pupils  take  the  second  case  of  addition ; 
the  second  should  follow  the  second  case  of  addition.  The 
pupil  should  be  first  taught  the  mechanical  method  of  doing 
the  work,  without  being  shown  the  reason  for  it  or  being  re- 
quired to  give  any  explanation  of  the  process.  A  general 
idea  of  "borrowing"  10  from  the  next  term  of  the  minuend, 
and  "carrying"  1  to  the  next  term  of  the  subtrahend,  may 
be  given  to  pupils  who  seem  prepared  to  understand  it ;  but 
QO  logical  solution  should  be  required  at  first. 


METHODS   OF   TEACHING. 

Course  of  Lessons. — The  course  of  lessons  in  Written  Sub- 
traction is  as  follows: 

1.  To  write  the  elementary  differences  of  tlie  subtraction  table. 

3.  To  subtract  numbers  of  two,  three,  etc.  terms,  when  there  ia 
lotliing  "to  borrow." 

3.  To  subtract  numbers  of  two  terms,  then  of  three  terms,  etc.,  when 
there  is  something  "to  borrow." 

4.  To  subtract  when  there  are  two  or  more  ciphers  in  the  minuend. 

Illustration. — The  method  of  subtraction  may  be  illus- 
trated by  bunches  of  little  sticks,  representing  tena,  hundreds, 
etc.,  and  showing  how  one  bunch  of  a  higher  denomination 
represents  ten  of  a  lower,  and  how  we  can  "  borrow"  one  of 
the  higher  and  unite  it  with  the  lower  denomination.  Little 
heaps  of  pebbles,  or  of  beans,  or  of  grains  of  corn,  and  boxes, 
real  or  imaginary,  may  also  be  used,  or  pictures  of  them  on 
the  board  representing  the  same.  These  may  be  of  some  aid 
to  the  beginner;  but  if  the  notation  has  been  thoroughly 
tauirht,  there  will  be  very  little  need  of  concrete  illustration. 
Let  the  student-teacher  give  a  lesson  on  the  subject. 

Explanation. — Young  pupils  should  first  be  taught  to  do 
the  work,  and  afterwards  be  required  to  explain  it.  The  ex- 
planation should  at  first  be  in  a  simple  form,  merely  indicating 
the  steps  of  the  mechanical  process.  Older  pupils  should 
give  a  full  logical  explanation.  There  are  two  methods  of 
explaining  the  second  case,  known  as  the  "method  of  borrow- 
ing" and  the  "  method  of  adding  ten,"  either  of  which  may 
be  employed  according  to  the  preference  of  the  teacher.  It 
is  difficult  to  decide  which  is  the  simpler,  though  teachers 
generally  prefer  the  method  of  "borrowing;"  and  when  there 
are  no  ciphers  in  the  minuend,  it  is  probably  the  simpler. 
When  there  are  several  ciphers  in  the  minuend,  the  method 
of  "adding  ten"  is  simpler.  The  latter  method  is  much  pre- 
ferred in  practice.  We  should  teach  a  pupil  to  subtract,  in 
practice,  by  adding  ten  to  the  upper  term,  and  adding  one  to 
the  next  higher  term  of  the  subtrahend,  though  many  pupils 
arc  practising  the  opposite  method  at  the  present  day. 


TEACHING    PRIMARY    ARITHMETIC.  859 

III.  Teaching  Multiplication  and  Division. 

As  soon  as  the  pupils  can  add  and  subtract  a  few  of  the 
smaller  numbers,  they  should  begin  multiplication  and  division. 
The  old  way  of  teaching  multiplication  was  to  begin  by  put- 
ting a  "  table-book "  in  the  hands  of  the  pupils,  and  requiring 
them  to  commit  the  multiplication  table.  What  the  table 
meant,  where  it  came  from,  what  it  was  for,  or  where  it  was 
going  to  or  going  to  lead  them,  they  knew  no  more  than  they 
did  of  the  origin  or  nature  of  a  sunbeam. 

Principles  of  Teaching. — There  is  a  better,  easier,  and 
more  natural  way;  and  this  way  we  will  suggest  in  the  follow- 
ing general  principles: 

1.  Maltiplication  should  be  taught  as  concise  addition. 
Thus  the  pupil  should  be  taught  that  two  2's  are  4,  because 
2  +  2=4;  or  that  two  3's  are  6,  because  3-|-3=6,  etc.  Instead 
of  the  pupil's  entering  upon  multiplication  as  a  new  and  in- 
dependent process,  he  will  thus  see  the  nature  of  the  subject 
and  its  logical  evolution  from  a  general  synthesis.  He  will 
see  the  origin  and  meaning  of  the  multiplication  table ;  and 
not  regard  it  as  a  mere  collection  of  abstract  names  and  num- 
bers to  be  committed  to  memory.  He  w'ill  be  able  to  make 
the  multiplication  table  for  himself,  and  will  see  the  reason 
for  committing  it  to  memory,  that  he  may  not  have  to  derive 
the  products  every  time  he  wishes  to  use  them. 

2.  Division  should  be  taught  as  reverse  multiplication. 
Division  can  be  taught  in  two  ways ;  as  concise  subtraction,  or 
as  reverse  multiplication.  That  is,  the  elementary  quotients 
may  be  obtained  by  a  process  of  subtraction,  or  by  reversing 
an  elementary  product.  Thus,  if  we  wish  to  show  a  pupil 
how  many  times  4  is  contained  in  12,  we  can  subtract  4  suc- 
cessively from  12  three  times  to  exhaust  12;  and  thus  infer 
that  4  is  contained  in  12  three  times.  We  can  also  derive  the 
quotient  from  the  consideration  that,  since  three  4's  are  12, 
12  contains  three  4's,  or  12  contains  4  three  times. 


300  METHODS   OF   TEACHING, 

Both  of  these  methods  are  legitimate,  but  the  method  of 
roverse  multii)lication  is  preferred  for  two  reasons.  First,  it 
is  the  more  convenient  in  practice,  since  the  elementary 
'/iiofients  can  be  immediately  derived  from  the  elementary 
/irodi/cts.  By  the  method  of  concise  subtraction,  we  should 
liave  to  derive  each  elementary  quotient  by  performing  several 
subtractions,  which  would  often  be  very  tedious.  Second,  it 
avoids  the  necessity  of  committing  a  division  table.  If  we 
derive  the  elementary  quotients  by  subtraction,  it  would  be 
necessary  to  arrange  them  in  a  table  and  commit  them,  as  we 
do  the  elementarj^  products ;  but  if  we  obtain  the  quotients 
by  reverse  multiplication,  we  can  derive  them  from  the  mul- 
ti[)lication  table,  and  will  not  need  any  table  of  division. 

3.  Multiplication  and  Division  should  be  taught  sim,ul- 
taneously.  This  is  suggested  by  the  logical  relation  of  the 
two  subjects.  The  two  ideas  are  so  intimately  related  that 
one  grows  directly  out  of  the  other.  Every  s^-nthesis  sug- 
gests naturally  its  opposite,  an  analysis.  A  multiplicative 
synthesis  can  hardly  be  made  without  the  intimation  of  its 
opposite,  a  divisionative  analysis.  Thus,  as  soon  as  the  pupil 
learns  that /bur  times  five  are  twenty,  he  is  prepared  to  see 
that  twenty  contains  five,  four  times.  The  method  suggested 
is  thus  founded  upon  and  indicated  by  the  laws  of  thought. 

It  is  also  much  more  convenient  to  present  the  subject  in 
this  manner.  The  same  fact,  a  product,  answers  a  double 
purpose ;  the  additive  process  which  determines  a  product, 
gives  also  the  materials  for  a  quotient.  In  practice  we  should 
have  the  pupil  commit  the  whole  of  "  one  column"  of  multi- 
plication before  we  have  them  derive  the  quotients.  This 
principle  applies  to  mental  multiplication  and  division,  and  to 
the  simple  written  exercises  which  represent  these  operations. 
In  written  multiplication  and  division  proper,  it  is  more  con- 
venient to  teacli  the  processes  separately.  Multiplication 
should  be  taught  first,  and  after  the  pupils  are  quite  familiar 
with  the  process,  they  should  pass  to  division 


TEACHING    PRIMARY    ARITHMETIC.  -  8ol 

3IufHplirafion  Tab^e. — The  Multiplication  Table  is  a  table 
of  the  elementary  products.  These  [)roducts  have  to  be  com- 
mitted to  memory.  This  is  not  an  easy  task;  indeed,  it  is 
one  of  the  most  ditticult  tasks  with  which  the  ^'oung  i)U()il 
meets.  It  requires  months  and  sometimes  years  for  the  child 
to  become  thoroughly  familiar  with  it.  In  the  early  history' 
of  arithmetic  in  Europe,  operations  were  often  pei'formed  in 
such  a  way  as  to  require  only  a  portion  of  the  multiplication 
table,  on  account  of  the  extreme  ditlicult}'  of  committing  the 
products  to  memor}'. 

How  shall  we  teach  a  child  the  table?  The  method  of  for- 
mer times  is  not  easily  forgotten.  The  book  was  put  into 
the  child's  hand,  and  sometimes  the  birch  upon  his  back, 
that  the  products  might  be  put  into  his  head.  Who  does  not 
remember  the  toil  and  the  trouble  ;  how  we  dreaded  the  result 
of  a  treacherous  memory  ;  how  we  rejoiced  in  "  five  times  " 
and  •'  ten  times  ;"  how  we  "  stuck"  on  **  9  times  7,"  and  "  7 
times  8,"  and  confounded  "  1 1  times  1 1,'*  and  *'  11  times  12;" 
and  how,  at  last,  through  great  tribulation,  we  scaled  the 
mount  and  stood  victor  of  a  hard-fought  battle  at  the  top?  Is 
there  a  better  wa^-  than  the  old  way? 

The  Method. — First,  pupils  should  make  the  multiplication 
table  for  themselves.  They  will  then  see  the  nature  and  use 
of  such  a  table,  and  will  study  it  with  more  interest  and  com- 
mit it  with  greater  ease.  Second,  when  thus  formed,  study, 
recitation,  frequent  repetition,  are  necessary  to  fix  it  in  the 
memory.  The  pupil  must  repeat  it  over  and  over,  and  be 
drilled  upon  it  until  he  knows  it.  Third,  writing  it  frequently 
on  the  slate  or  blackboard,  will  assist  the  pupil  in  committing 
it  to  memor}-.  The  seeing  of  it  will  tend  to  fix  it  upon  the 
visual  memory,  which  is  often  better  than  attempting  to  fix  it 
in  the  oral  memory.  The  eye  will  aid  the  ear  in  making  the 
acquisition.  Fourth,  reciting  the  table  in  concert  will  also  aid 
in  learning  it.  It  gives  animation  and  zest  to  the  recitation, 
and  deepens  the  impression  through  the  increase  of  interest. 
16 


362  METHODS    OF   TEACHING. 

The  duller  pupils  will  thus  learn  also  from  the  brighter  pupils 
The  frequent  hearing  of  the  names  associated  together  will  at 
last  make  a  permanent  connection  between  the  factors  and 
the  [)roducts,  so  that  as  soon  as  we  think  of  one,  the  other 
will  occur  to  us.  Fifth,  the  singing  of  the  table  to  a  little 
tune  is  also  recommended.  This  has  been  practiced  by  many 
teachers,  and  with  good  results.  It  is  a  pleasant  exercise,  and 
the  pupil  is  learning  a  lesson  while  amusing  himself  with  a 
song.  Tliere  are  several  little  tunes  to  which  the  words  may 
be  fitted  ;  among  the  best  is  one  known  as  "Sparkling  Water," 
or  "  Old  Dan  Tucker,"  a  coarse  name  for  a  beautiful  melody. 

Division  Table Should  a  division  table  be  committed  to 

memory'  ?  It  has  been  the  custom  of  many  teachers  to  have 
their  pupils  study  and  commit  a  table  of  quotients  after  they 
have  committed  a  multiplication  table.  This,  however,  is  not 
necessary,  if  division  is  taught  as  reverse  multij^lication. 
The  multiplication  table  gives  also  the  quotients,  the  product 
being  regarded  as  the  dividend,  and  the  two  tactors  as  divisor 
and  quotient.  If,  however,  division  be  taught  as  concise  sub- 
traction, it  will  be  necessary  for  a  i)upil  to  commit  a  division 
table,  as  he  has  no  method  of  determining  a  quotient  but  bj' 
subtracting,  or  remembering  it  from  a  table. 

Course  of  Lessons. — The    course    of    lessons   in    Primary 
Multiplication  and  Division  is  as  follows: 

1.  Lead  the  pupil  to  a  clear  idea  of  "times,"  and  then  of  a  numbei 
taken  several  times. 

2.  Lead  the  piii)il  to  make  the  table  of  "two  times,"  and  have  him 
coniinit  it . 

'6.  Apply  the  table  of  "two  times,"  in  solving  little  problems  like  "If 
one  orange  costs  3  cents,  what  will  2  oranges  cost?" 

4.  Lead  the  pupil  to  derive  quotients  from  "two  times,"  and  to  apply 
tliese  quotients  to  solving  little  problems. 

5.  Proceed  in  the  Siime  way  with  "three  times,"  "  four  times,"  etc., 
'ip  to  "  twelve  times,"  deriving  the  quotients  from  each  multiplication 
column. 

6.  Drill  the  pupils  on  M'riting  and  reciting  the  multiplication  table 
until  they  have  committed  it. 


TEACHING    PRIMARY    ARITHMETIC.  363 

Model  Lesston. — How  many  times  do  you  recite  in  a  day?  How  many 
times  does  the  clock  stril<e  at  noon  ?  If  you  have  2  cents  in  one  hand  and 
2  cents  in  the  other  hand,  how  maay  times  2  cents  have  you?  How 
many  cents  have  you  ?  How  many  cents  then  are  two  times  2  cents?  If 
I  move  3  balls  over  on  this  wire  of  the  numeral  frame,  and  then  move 
three  balls  more,  how  many  times  3  balls  have  I?  How  many  balls  in 
all  ■/  How  many  then  are  Iloo  times  3  balls  ?  Write  4  on  the  board  and 
then  write  4  under  it.  How  many  times  have  you  writ- 
ten 4?     How  many  are  4  and  4?     How  many  then  are  two        ~^        , 

2x2=4 
times  Al     Proceed  in  a  similar  manner  up  to  2  times  12.         9v3=6 

Then  have  them  write  the  multiplication  table  on  the  board,         2x4=8 
using  the  signs  X    and  =  as  in  the  margin.     When  the        etc.  etc 
pupils  know  ihe pi-vducts  of  "2  times,"  reverse  ihe  process 
for  the  quotients,  thus  :  How  many  2'smake  4?  4  then  is  how  many  2's? 
4  then  co;<tai/i6- how  many  2's?     -i  then  eontains  2  how  rnany  times?     2 
then  is  contained  in  4  how  many  times?    Proceed  in  a  similar  manner 
with  the  other  quotients  drawn  from  "two  times."      Then  have  the 
division  table  written  on  the  board,  using  the  symbols  -4-  and  =. 

After  the  pupils  are  familiar  with  the  process  of  deriving  tlie  multi- 
pliciition  table  by  addition,  lead  them  to  see  that  they  can  obtain  the 
successive  products  by  increasing  the  last  product  by  the  number  multi- 
plied to  find  the  next  product.  Thus,  when  thej'  have  "6  times  4  are 
24,"  ihey  can  obtain  7  times  4  by  adding  4  to  the  24,  making  28,  etc. 
Many  pupils  will  see  this  for  themselves;  those  who  do  not  should  be 
led  to  see  it  by  the  teacher. 

Practical  ExercLsc. — To  make  pupils  rapid  and  accurate 
in  the  mechanical  processes  of  adding,  subtracting,  multiply- 
ing, and  dividing,  the  following  exercise  is  practiced  by  some 
teachers,  with  excellent  results: 

Let  the  teacher  write  four  columns  of  figures  on  the  blackboard,  as  is 
represented  in  the  margin,  the  first  column  be- 
ing additive,  the  next  subtractive,  etc.,  as  is  in-  (+)  (~)  (X)  (-r-) 
dicated  by  the  symbols  placed  above  them.  The 
teacher,  with  the  pointer,  will  point  out  certain 
figures,  the  corresponding  numbers  being  added, 
subtracted,  multiplied,  ordivided,  as  is  indicated 
by  the  symbol  at  the  head  of  the  column.  Care, 
of  course,  must  betaken  not  to  require  a  division 
by  a  number  that  is  not  exactly  contained.  This 
exercise  may  be  con;iuued  for  many  recitations, 
in  connection  with  the  other  lessons,  with  great  advantage  to  the  pupils. 


1 

1 

1 

I 

2 

2 

2 

2 

3 

3 

3 

3 

4 

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4 

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5 

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6 

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6 

7 

7 

7 

7 

8 

8 

8 

8 

9 

9 

9 

9 

oOi  METHODS   OF  TEACHING. 

Written  Multiplication. — The  pupils  should  write  the 
elementaiy  products  and  quotients  as  they  are  learning  them. 
When  they  are  familiar  with  the  table,  they  are  ready  to  learn 
written  multiplication  and  division,  properly  so  called.  These 
should  be  taught  separately,  like  written  addition  and  sub- 
traction. We  should  begin  with  multiplication  and  drill  the 
pupils  upon  it  until  they  are  quite  familiar  with  the  process 
of  mnltiplj'ing. 

Course  of  Lessons. — The  subject  should  be  i)rcsented  in 
two  cases  ;  first,  ^chen  the  multiplier  does  not  exceed  twelve, 
and  second,  ivhen  it  does  exceed  ttvelve.  These  two  cases  will 
include  the  following  classes  of  problems: 

1.  Write  the  elementary  products  in  the  usual  form  of  written  multi- 
plication. 

2.  Multiply  when  the  multiplicand  consists  of  several  terms,  but  not 
requiring  any  "Ciirrying;"  as,  214  multiplied  by  2. 

3.  Multiply  when  the  multiplicand  consists  of  several  terms,  the  mul- 
tiplier being  one  term,  and  the  products  require  "carrying,"  as,  368  by  2. 

4.  Multiply  when  there  are  two  or  more  terms  in  the  multiplier;  as, 
457  by  23. 

5.  Multiply  when  there  are  one  or  more  zeros  in  the  multiplier. 

6.  Multiply  when  there  are  one  or  more  zeros  at  the  right  of  either  or 
both  multiplier  and  multiplicand. 

Explanation. — The  pupils  should  first  be  required  to  do 
the  work  without  giving  any  explanation  of  the  process. 
When  they  have  become  familiar  with  the  operation,  they 
va.VLy  be  required  to  state  the  different  steps  of  the  process 
without  ffivins;  the  reason  for  the  same.  This  is  what  is  called 
the  simple  form  of  solution.  Advanced  pupils  should  be  re- 
quired to  give  a  full  logical  solution,  in  which  the  reason  for 
each  step  is  logiealh^  stated.  For  the  simple  form,  see  the 
author's  Primary  and  Elementary  Arithmetics;  for  the  full 
solution,  see  the  author's  Written  Arithmetic. 

Written  Division. — The  first  lesson  in  written  division 
consists  in  writing  the  elementary  quotients  as  they  are  learned 
in  the  mental  exercises;   when  he  is  familiar  with  these,  he 


TEACHING   PRIMARY    ARITHMETIC.  o6o 

ma^'  take  up  written  division  proper.  The  fundamental  prin- 
ciple in  teachino^  written  division  is,  tliat  short  and  long 
divisioti  should  be  taught  together,  almost  from  the  beginning. 
Let  the  pupils  see  that  they  are  merely  different  ways  of  writ- 
ing the  results.  It  will  be  well  even  to  have  him  express  the 
elementary  quotients  by  both  methods.  This  will  avoid  the 
diflBculty  that  pupils  usuallj'  experience  in  making  the  transi- 
tion from  "  short"  to  "  long"  division. 

Course  of  Lessons. — The  difficulty  of  teacliing  written  di- 
vision will  be  greatl}^  lessened  by  a  careful  grading  of  the 
exercises. 

1.  Express  the  elementary  quotients. 

2.  When  there  are  several  terms  in  the  dividend  and  quotient,  but 
when  there  are  no  remainders;  as,  248  divided  by  2. 

3.  When  there  are  remainders,  the  divisor  still  not  exceeding  twelve  ; 
as,  17  divided  by  3. 

4.  When  the  divisor  exceeds  twelve;  as,  156  divided  by  13. 

5.  When  tliere  are  one  or  more  ciphers  in  the  quotient;  as,  3456  di- 
vided by  32. 

6.  When  there  are  ciphers  at  the  right  of  the  dividend  and  then  at  the 
right  of  the  divisor,  and  then  at  the  right  of  both. 

In  the  first  three  classes,  the  problems  should  be  solved  by 
both  "  short"  and  '' long"  division.  In  the  fourth  class,  we 
must  solve  by  "  long"  division.  The  divisors  should  be  graded, 
beginning  at  13,  and  passing  on  to  14,  15,  16,  17,  etc.  The 
difficulty  which  will  now  be  met  by  the  pupil  is  to  ascertain 
the  terms  of  the  quotient.  The  teacher  must  lead  him  to  test 
his  quotient  terms  by  the  following  considerations  : 

1.  Tlie  pupil  will  notice  that  there  are  four  steps  in  the  operation : 
1st,  Divide;  2d,  Maltipli/  ;  3d,  Subtract;  4th,  Bring  down. 

2.  If,  when  we  multiply,  the  product  is  greater  than  the  partial  divi- 
dend, the  quotient  term  is  too  large  and  must  be  diminished. 

3.  If,  when  we  subtract,  the  remainder  is  not  less  than  the  divisor, 
the  quotient  term  is  too  small  and  must  be  increased. 

Explanation. — As  in  multiplication,  the  pupil  should  be 
required  to  do  the  work  at  first  without  giving  explanation 
of  the  process.     He  should  afterward  be  required  to  state  the 


366  METHODS   OF   TEACHING. 

Steps  of  the  process  without  giving  the  reasons  for  the  steps. 
When  he  is  sufficiently  advanced,  he  should  he  required  to 
give  a  full  logical  solution,  such  as  is  found  in  the  author's 
arithmetics. 

The  Grubc  Method. — There  is  a  method  of  teaching  the  ele- 
mentary sums,  differences,  products  and  quotients  used  in  Ger- 
manv,  and  highly  recommended  bv  a  number  of  American  edu- 
cators,  called  the  Gruhe  Method.  The  principle  of  this  method 
is,  that  it  makes  each  individual  number,  instead  of  the  operations, 
the  basis  of  the  instruction ;  and  combines  in  each  lesson,  from 
the  start,  the  four  fundamental  operations. 

Thus,  in  treating  any  number,  "  all  the  operations  possible 
within  the  limits  of  this  number"  are  presented  in  the  same  les- 
son. That  the  method  may  be  understood  the  lessons  on  a  few  of 
the  first  numbers  are  presented. 

The  Number  2. — The  exercises  on  Tico  are  as  follows : 

2=1+1;  2-1=1;  2-2=0. 

2=2X1 ;  2=1X2;  2h-1=2;  2^2=1. 
The  Number  3.— The  exercises  on  Three  are  as  follows: 

3=1  +  1+1;  3=2+1  ;  3=1+2;  3—1=2;  3—2=1;  3—3=0. 

3=3X1 ;  3=1X3  ;  3^1=3  ;  3h-3=1. 
The  Number  4. — Tlie  exercises  on  Four  are  as  follows : 

4=1  +  1  +etc. ;  4  =3+1 ;  4=2+2 ;  4-1=3 ;  4-2=2 :  4—3=1 ;  4—4=0. 

4=4X1 ;  4=1X4:  4=2X2  ;  4^1  =  1;  4^4=1  ;  4^2=2. 
The  >  umber  5. — The  exercises  on  Five  are  as  follows  : 

5=l+l+etc.;  5=4-hl  ;  5=3+2;  5=2+3;  5=1+4;  etc. 

5-1=4 ;  5—2=3  ;  5  -3=2;  5-4=1 :  5—5=0. 

5=,5X1 ;  5=1X5;  5^1=5  ;  5^5=1. 
The  Number  6. — Tlie  exercises  on  Six  are  as  follows  : 

6=l+l+etc.;  6=5+1  ;  6=1+2;  6=3+3 ;  6=2+4 ;  6=1+5;  etc. 

6—1=5;  6-2=4;  6—3=3;  6—4=2;  6—5=1 ;  6—6=0. 

6=6X1 ;  6=1X6;  6=3X2;  6=2X3. 

6h-1=6;  6h-6=1;  6h-2=3  ;  6^3=2. 
The  Number  7.— The  exercises  on  Seven  are  as  follows : 

7=l+l-retc.:  7=:=6+l;  7=.5+2 ;  7=4+3 ;  7=3+4;  7=2+5;  etc. 

7—1=6 ;  7-2=5;  7—3=4;  7—4=3  ;  7—5=2  ;  7— «=1 ;  7—7=0. 

7=7X1 ;  7=1X7  ;  7-1=7  ;  7^7=1. 


TEACHIXG    PRntARY    ARITHMETIC.  SGiT 

Similar  exercises  are  presented  on  tlie  numbers  in  regular  order 
as  far  as  100  or  144.  comprising  the  entire  multiplication  table  with 
the  corresponding  quotients. 

Experienced  teachere  of  this  method  suggest  that  beginners 
should  complete  the  exercises  as  far  as  10  the  first  year;  as  far  as  20, 
the  second  year;  as  far  as  100  the  third  year,  etc.  Some  teachers 
combine  the  fractional  parts  of  numbers  with  the  above  exercises. 

The  nature  of  the  Grube  Method  may  be  more  clearly  seen  by 
comparing  it  with  the  Xormal  Method  previously  given. 

1.  The  Gi-ube  Method  makes  number  the  basis  of  arithmetical  in- 
struction :  the  Xormal  Method  makes  ajjerations  on  numbers  the 
basis.  The  leading  object  of  the  former  is  to  comprehend  numbers ; 
tlie  object  of  the  latter  is  to  use  or  operate  with  numbere. 

•2.  The  Grube  Method  proceeds  by  analysis  from  a  number  to  its 
parts;  the  Normal  Method  proceeds  by  synthesis  from  the  ijarts  of 
the  number  to  the  number. 

3.  The  Grube  Method  requires  llie  learner  to  comprehend  and 
operate  with  the  four  fundamental  rules  from  the  beginning;  the 
2s  ormal  Metliod  teaches  the  two  correlative  processes  of  addition 
and  subtraction  together;  and  subsequently  the  two  correlative 
processes  of  multiplication  and  divi.sion  together. 

4.  The  exercises  of  the  Grube  ^lethod  u^ed  in  teaching  addition, 
subtraction,  etc..  are  used  in  the  Xormal  Method  after  the  pupil 
learns  to  add.  subtract,  multiply  and  divide. 

Note. — Space  does  not  prrrnit  a  discussion  of  the  relative  merits  of  the 
two  methods.  An  enthusiastic  teacher  who  has  faith  in  his  method,  will 
succeed  in  teaching  the  elenient^iry  sums,  ditfereuces,  products,  and  quo- 
tient? with  either.  By  the  Xormal  Method  these  may  be  taught  in  a  little 
more  than  a  year ;  teachers  of  the  other  method  usually  devote  three  years 
to  the  subject. 

lY.   Teaching  Common  Fractions. 

After  the  pupils  are  somewhat  familiar  with  the  funda- 
mental operations,  they  are  ready  to  begin  the  subject  of  Com- 
mon Fractions.  In  teaching  Fractions,  the  teacher  should  be 
guided  by  the  following  general  principles  : 

Principles. — 1.  The  first  lessons  in  fractions  should  be 
given  orally.  So  text-book  is  needed  in  teaching  the  pri- 
mary ideas  of  the  subject.  The  teacher  should  drill  the 
pupils  for  several  daj-s  before  taking  up  the  subject  in  the 
i)ook. 


C)(j3  METHODS   OF   TEACHING. 

2.  Mental  and  written  e.rercines  nhonld  be  combined  in  the 
first  let^sons.  The  order  is,  first  the  idea,  then  the  oral  ex- 
pression of  it,  and  then  the  written  ejrjiression  of  it.  As  soon 
as  the  pupil  has  an  idea  of  an  operation,  he  should  be  taught 
to  express  it  in  written  characters.  The  seeing  of  the  opera- 
tion will  help  to  make  it  clear  to  the  understanding  and  fix 
it  in  the  memory. 

3.  The  elements  of  fractions  should  be  taught  by  means  of 
risible  objects.  The  pupil  should  he  led  to  see  the  fractional 
idea  and  relation  in  the  concrete,  Ijefore  he  is  required  to  con- 
ceive it  abstractly.  The  olvjects  to  be  employed  are  apples, 
lines,  or  circles  on  the  blackboard,  etc.  An  arithmetical 
frame,  with  long  rods  cut  in  sections,  is  used  in  the  schools 
of  Sweden,  Prussia,  etc. 

4.  The  operations  in  written  fractions  should  be  taught  to 
young  pupils  mechanically.  They  sliould  be  drilled  upon  the 
operations  until  they  are  thoroughly  familiar  with  them,  even 
before  they  understand  fully  the  reason  for  such  operations. 
This  is  in  accordance  with  the  principle  that,  with  young  pu- 
pils, practice  should  precede  theory. 

5.  The  Methods  or  Rules  in  fractions  should  be  derived  by 
analysis  and  induction.  Special  problems  should  be  given 
for  solution,  and  the  rules  or  methods  of  operation  be  inferred 
from  the  analysis  of  these  problems.  The  principles  of  frac- 
tions should  be  first  illustrated  rather  than  demonstrated. 
These  principles  should  be  committed,  and  the  pupil  should 
learn  to  apph'  them  readily. 

Tfiinfjs  to  be  Taufiht The  several  things  to  be  taught  in 

fractions  are  as  follows  : 
1.  Tl)e  idea  of  caA  fraction. 
2    The  fractional  parts  of  numbers. 

3.  Solution  of  problems  requiring  the  fractional  parts  of  numbers. 

4.  The  notation  of  fractions. 

5.  Analysis  of  concrete  problems. 

6.  The  cases  of  reduction  of  fractions,  and  their  analysis. 

7.  Addition,  subtraction,  multiplication,  and  division  of  fractions. 
S.  Th^  rules  and  the  principles. 


TEACHING    PRIMARY    ARITHMETIC.  o(J'J 

1.  Idea  of  a  Fraction. — First,  give  a  lesson  on  one-half ; 
then  on  one-third  ;  then  on  one-fourth^  etc.,  as  tar  as  one-tenth. 
The  method  is  shown  in  the  following  model  lesson  :     ' 

Model  r,f'ssi}n. — If  I  divide  an  apple  into  two  equal  parts,  what  is  one 
part  called  ?  What  are  two  parts  called?  How  many  halves  in  a  whole 
apple?  What  Is  one-half  of  anything?  Ans.  One-half  of  ajiylhing  is 
one  of  the  two  equal  parts  into  which  it  may  be  divided. 

2.  Applij  to  Numbers. — The  next  step  is  to  apply  the 
fractional  idea  to  finding  the  parts  of  numbers.  This  is  a 
logical  step  in  adv%ance:  the  first  step  was  to  get  a  part  of  a 
unit ;  now  we  pass  to  finding  parts  of  collections  of  units. 
To  illustrate,  supi)ose  we  wish  to  obtain  the  one-half  of  6. 
Show  the  pupil  that  one  of  the  two  equal  parts  of  6  is  3,  hence 
3  is  one  half  of  6.  We  then  proceed  to  obtain  one-half 
of  other  numbers,  from  2  to  24;  then  get  one-third  and  two- 
thirds  of  numbers,  also  one-fourth.^  two-fourths^  etc.,  of  num- 
bers, etc.  The  next  step  is  to  find  the  fractional  parts  of 
numbers  which  do  not  give  exact  parts ;  as  ^  of  7,  ^  of  11,  etc. 

After  the  pupil  has  the  idea,  he  should  be  required  to  give 
a  simple  solution  of  the  process.  Two  forms  of  solution  are 
suggested,  one  resting  on  multiplication,  the  other  on  division. 
The  latter  will  be  more  convenient  in  practice,  as  in  finding 
one-half,  one-third,  etc.,  of  large  numbers,  we  must  divide 
them  by  two,  three,  etc.  The  thought  is,  that  to  find  one- 
half  of  a,  number,  we  divide  the  number  into  two  equal  parts. 

Model  Lesson. — Problem.  What  is  one-half  of  6?  Solution.  One- 
half  of  6  is  3,  because  2  times  three  are  6.  Sol.  2d.  One-half  of  6  is 
3,  because  6  divided  by  3  is  3.  Illustration.  6=34-3;  hence  3  is  one  of 
th^  two  equal  parts  of  6,  and  3  is  therefore  one-half  of  6.  We  should  also 
get  two,  three,  etc.,  fractional  parts  of  numbers.  Prob.  What  are  two- 
thirds  of  6  ?  Sol.  One-third  of  6  is  2,  and  two-thirds  of  6  are  two  times 
2,  which  are  4 ;  therefore,  two-thirds  of  6  are  4.  Prob.  What  is  i  of  7  ? 
Sol.    7  equals  6+1  ;  J  of  6  is  3,  ^  of  1  is  ^,  etc. 

3.  Concrete  Problems. — The  next  step    is  to  appl}^  these 

fractions  to  concrete  problems.     Thus,  "  If  A  has  6  apples 

and  B  has  one-half  as  many,  how  many  apples  has  B?"     The 

pupil  should  be  required  to  give  a  clear  and  simple  solution. 

16* 


370  METHODS   OF   TEACHING. 

lllustratLon. — Prob.  If  A  has  6  apples  and  B  lias  one-half  as  many, 
how  many  apples  has  B  ?  Solution.  If  A  has  6  apples  and  B  has  one- 
half  as  many,  B  has  one-half  of  6  apples, or  3  apples.  Prob.  If  I  have  9 
marbles  and  give  2  thirds  of  them  away,  how  many  will  I  give  away? 
Solution.  If  I  have  9  marbles  and  give  2  thirds  of  Iheni  away,  I  give 
away  2  thirds  of  9  marbles;  one  third  of  9  marbles  is  3  marbles,  and  3 
thirds  are  2  times  3  marbles,  or  6  marbles. 

4.  The  Xotation. — The  next  step  is  to  present  the  notation 
of  fractious.  This,  in  practice,  may  be  done  in  connection 
with  some  of  the  previous  exercises.  The  notation  may  be 
presented  in  two  ways.  The  teacher  may  simply  state  the 
method  of  writing  the  numerator  and  denominator,  and  drill 
the  pupils  in  writing  until  they  can  read  and  write  fractions 
readily.  By  this  method  pupils  will  see  no  reason  for  the 
method,  and,  indeed,  will  not  think  to  inquire  after  any  reason. 
It  will  be  purely  arbitrary  and  conventional  to  them. 

Another  method  is  to  lead  the  pupil  gradually  to  the  nota- 
tion, somewhat  as  we  may  supix)se  it  was  reached  historically. 
Thus,  we  ma}''  write  some  fraction,  as  3-/ourths,  then  abbre- 
viate it  to  3-4ths,  then  still  further  abbreviate  by  omitting  the 
ths,  giving  3-4 ;  then  represent  it  by  separating  the  3  and  4 
by  an  oblique  line,  as  V4 ;  ^"cl  then  let  this  line  crowd  the  4 
down  under  the  3  and  leave  |.  Or,  we  might  have  the 
name  written  under  the  numerator,  as,  __? —  ;  then  abbreviate 

'        '  fourths  ' 

it  into  -?_,  and  then  as:ain  into  f.     Let  the  teacher  illustrate. 

5.  Atmlysis The  next  step  is  to  apply  the  fractions  in 

the  analysis  of  two  or  three  classes  of  concrete  problems,  as 
follows:  1.  "If  2  apples  cost  4  cents,  what  cost  3  apples?" 
2.  "  What  will  3  yards  of  ribbon  cost,  if  |  of  a  yard  cost  8 
cents?"     3.  "Six  is  |  of  what  number?"  etc. 

lllustratian. — 1.  Prob.  If  2  apples  cost  4  cents,  what  cost  3  apples? 
Sol.  If  2  apples  cost  4  cents,  1  apple  costs  i  of  4  cents,  which  is  2  cents, 
and  3  apples  cost  3  times  2  cents,  which  are  6  cents.  2.  Prob.  What 
will  3  yards  of  ribbon  co.st,  if  |  of  a  yard  cost  8  cents?  Sol.  If  f  of  a 
yard  cost  8  cents,  |  of  a  yard  costs  i  of  8  cents,  or  4  cents,  and  f,  or  1 
yard,  costs  3  times  4  cents,  or  12  cents;  and  if  1  yard  costs  12  cents,  3 


TEACHING    PRIMARY   ARITHMETIC. 


371 


yards  cost  3  times  12  cents,  or  36  cents.  3.  Prob.  Six  is  f  of  what  num 
ber?  Sol.  If  6  is  |  of  some  number,  1  of  the  number  is  ^  of  6,  or  3,  and 
|,  or  the  number,  is  3  times  3,  or  9. 

6.  liediution  of'  Fractionts. — Tho  next  step  is  to  present 
some  of  the  simpler  cuses  iu  the  reduction  of  fractions.  The 
several  cases  of  R-eduction  are:  1.  A  number  to  a  fraction; 
2.  A  fraction  to  a  number;  3.  To  higher  terms;  4.  To  lower 
terms;  5.  Compound  fractions  to  simple;  6.  To  common 
denominator.  We  should  present  these  casies  first  concretely 
by  illustration,  and  then  require  the  pupils  to  give  a  simple 
solution  of  the  problems.  We  shall  illustrate  with  a  few  of 
the  simpler  cases. 

Illustration. — Take  the  problem,  "How  many  sixths  inf  ?"  We  may 
illustrate  this  bj  circles  or  lin-es  on  the  board. 
In  the  first  circle,  we  have  three  equal  parts, 
and  two  q:'  them  are  two-tldrds.  Dividing 
these  thirds  into  two  equal  parts,  we  see  that 
we  have  six  equal  parts,  and  each  part  is  one- 
sixth  ;  and  we  see  that  the  two-thirds  contain 
four  sixths;  hence,  we  see  that  |  equal  4. 
The  same  thing  is  shown  with  the  two  lines,  in  which  the  distance  be- 
tween the  two  parallel  horizontal  lines  iudiciites  the  unit.  By  reversing 
this,  we  may  illustrate  how  to  reduce //•<>/«  higher  to  lower  terms. 

By  a  similar  illustration  we  Gin  show  how  to  reduce  a  compound  frac 
tion  to  a  simple  one.  To  illustrate,  take  the  problem,  "  What  is  i  of  ^?  " 
Divide  the  circle  into  four  equal  parts;  each  part  is  one-fourth.  To  ob- 
tiiin  k  of  one-fourth,  we  must  divide  each 
fourth  into  two  equal  parts.  Doing  this,  we 
find  we  have  eight  parts  in  the  circle;  hence 
each  part  is  ()/>.c-fi^7A^/i;  hence  one-Imlf  oi  one- 
fourth  is  one-eighth.  The  line  may  also  be 
used;  the  line  in  the  margin  illustmtes  finding  one-half  oi  one-third.  The 
teacher  should  make  constant  use  of  these  illustrations,  and  require  the 
pupils  also  to  illustrate  the  problems. 

7.  Analysis  in  Fractions. — The  pupils  should  learn  the 
anali/ses  of  these  cases  of  fractions.  These  analyses  should  be 
simple  and  concise.  They  are  designed  to  state  the  steps  of 
the  judgment  in  obtaining  the  results  required.     In  these  an- 


372  METHODS   OF   TEACHING. 

alyses,  the  unit  is  made  the  basis  of  reasoning;  it  is  a  centre 
around  which  the  reasoning  revolves.  We  present  the  analy- 
sis of  a  few  of  the  eases. 

Case  I.  is  to  reduce  a  number  to  a  fraction.  Prob.  How  many  fourths 
in  2|?  Sol.  In  one  there  are  4  fourths,  and  in  2  there  are  2  times  |  or  J ; 
and  I  plus  f  are  J^.  Case  II.  Is  the  reverse  of  this.  Pkob.  In  V  how 
many  oneal  Sol.  In  one  there  are  |,  hence  in  ^-  there  are  as  many  ones 
as  4  is  contained  times  in  11,  which  are  2|.  Another  solution  of  this 
second  case  is  as  follows  :  In  one  there  are  four  fourths;  hence  \  of  (he 
number  of /owr^/io  equals  the  number  of  onfs;  }  of  11  equals  2|.  '1  lie 
first  of  these  is  much  more  easily  understood  by  cliildren. 

Case  III.  is  to  reduce  to  hUjher  terms.  Pkub.  In  |  how  many  sixths? 
Sol.  In  one  there  are  %  and  in  i  there  are  \  of  °,  or  I,  and  in  |  there  are 
2  times  f ,  or  I.  Case  IV.  is  the  rever.se  of  this,  to  reduce  to  lower  terms. 
Prob.  In  %  how  many  thirds?  Sol.  In  one  there  are  f,  in  one-third 
there  are  \  of%,  or  two-sixths,  hence  in  |  there  are  as  many  thirds  as  | 
are  contained  times  in  ^,  or  |.  This  case  also  leads  to  the  reducing  to  a 
common  denominator,  in  which  the  analysis  is  likethatjust  given. 

Case  V.  is  the  reducing  a  compound  fraction  to  a  simple  one.  Puob. 
What  is  I  of  I  ?  Sol;  One-third  is  one  of  the  three  equal  parts  into  which 
a  unit  is  divided;  if  each  third  is  divided  into  two  equal  parts,  three  thirds, 
or  the  unit,  will  he  divide  1  into  three  times  two,  or  six  equal  parts,  and 
each  part  will  be  one-sixth  of  a  unit;  hence  J  of  |  is  ^.  Another 
Solution.  One  third  equals  |,  and  \  of  |  is  i;  hence  \  of  \  is  ^. 

The  first  solution  is  a  little  diflScult  for  a  beginner;  but  it  involves 
precisely  the  mental  process  of  obtaining  i  of  },  and  is  the  one  which 
should  be  used  when  a  child  is  ready  for  an  analysis.  The  second  solu- 
tion does  not  show  why  4  of  |  is  \,  though  it  obtains  the  result.  It  may 
be  used  with  the  beginner,  hut  it  should  be  afterward  followed  by  the 
other  solution.  A  celebrated  author  of  Mental  Arithmetic  gave  the  fol- 
lowing solution  :  "One-half  of  one  is  \,  and  if  i  of  one  is  i,  i  of  |  is  ^  of 
\,  which  is  ^."  The  error  in  this  logic  is  that  to  explain  what  is  "i 
of  |,"  the  author  assumes  he  knows  what  "^  of  ^"  is,  the  more  difficult 
thing  of  the  two. 

8.  The  Other  Cases. — All  the  other  eases  of  Fractions, — 
Addition,  Subtraction,  Multiplication,  Division,  and  Relation 
of  Fractions, — should  be  solved  by  analysis,  as  the  pupils 
become  able  to  understand  them.  The  student-teacher  should 
be  required  to  show  how  to  give  the  instruction.  Illustrate 
both  the  inductive  and  deductive  methods. 


TEACHtXG    PRIMARY    ARITHMETIC.  373 

9.  The  Rules. — The  pupil  needs  to  be  able  to  derive  results 
without  going  through  tlie  anal3'Sis  each  time,  and  for  this 
purpose  Rules  should  be  drawn  from  these  analyses.  These 
may  be  derived  by  inference  or  induction.  Thus,  in  reduc- 
ing 2|  to  fourths,  since  in  the  analysis  we  take  the  product 
of  4  and  2  and  add  the  3,  for  the  number  of  fourths,  we  may 
infer  the  rule,  "To  reduce  a  mixed  number  to  a  fraction,  we 
multiply'  the  integer  by  the  denominator  of  the  fraction,  and 
add  the  numerator  to  the  result,"  etc.  The  other  rules  of 
fractions  may  be  derived  in  the  same  way.  Another  method 
is  to  derive  them  from  the  principles  of  fractions.  The  in- 
ductive method  is  easier  for  learners,  and  is  prefei-red  in 
primary  arithmetic.  With  beginners,  however,  it  may  be  well 
to  teach  the  method  of  doing  the  work,  without  giving  any 
reason  for  it;  and  subsequently,  when  they  are  familiar  with 
the  rules,  the}'  may  learn  to  derive  them.  Let  the  student- 
teacher  give  examples  of  each  case  of  fractions,  and  show 
how  to  analyze  the  problems  and  derive  the  rules. 

10.  The  Principles. — After  pupils  are  somewhat  familiar 
with  these  fundamental  ideas  and  processes,  they  should  be 
taught  the  pi'inciples  of  fractions.  These  principles  may  be 
illustrated  so  that  the  pupils  may  have  a  general  idea  of  the 
manner  in  which  they  are  derived,  or  pupils  may  be  required 
to  commit  and  apply  them  without  any  idea  of  how  the}'  are 
derived.  A  simple  solution  like  the  following  may  be  given: 
"  Multiply  the  denominator  of  |  by  2."  Sol. — If  we  multiply 
the  denominator  of  |  by  2,  we  have  3  eighths,  which  is  one- 
half  as  much  as  3  fourths,  since  eighths  are  only  half  as  great 
as  fourths;  from  which  we  infer  that  multiplying  the  denom- 
inator by  2  divides  the  fraction  by  2.  When  the  pupil  is 
ready  to  understand  the  demonstration  of  the  principles,  a 
real  demonstration  should  be  given,  and  not  some  loose,  in- 
definite statement,  such  as  we  find  usually  presented.  For 
the  more  general  demonstration,  see  the  Treatment  of 
Fractions  in  arithmetics. 


374  METHODS   OF   TEACHING. 

The  Student-teacher  should  now  be  required  to  outlice  the 
course  of  instruction  in  Fractions  in  primary  arithmetic,  and 
show  by  model  lessons  how  he  would  teach  them. 

V.    Teaching  Denominate  Numbers. 

Pi'iuciples  of  Insfrnction. — In  giving  instruction  in  De- 
nominate Numbers,  teachers  should  be  governed  b}-  the  fol- 
lowing principles: 

1.  Denominate  Ninnhers  should  be  taught  concretely.  The 
teacher  should  have  the  actual  measures  to  illustrate  the  sub- 
ject. If  they  are  not  in  the  school-room,  the  teacher  can  pro- 
cure them  at  a  trifling  expense.  In  some  text-books  on  pri- 
mary arithmetic,  we  find  pictures  of  the  measures;  but  the 
measures  Ihemselces  are  worth  much  more  than  the  pictures 
of  them.  In  fact  the  picturr^s  give  an  inadequate  idea  of  the 
measures,  and  often  an  incorrect  one.  The  neglect  of  this 
principle  is  very  common.  Most  teachers  have  the  pupils  re- 
peat the  tables  without  any  illustration  of  their  meaning. 
The  result  is,  that  these  "weights  and  measures"  are  to  manj- 
pupils  merely  so  many  words  without  any  corresponding 
defiuite  ideas. 

2.  The  teacher  should  require  the  pupils  to  make  a  practi- 
cal application  of  these  measures.  He  should  drill  them  on 
measuring  and  judging  of  the  length  of  rooms,  the  height  of 
ceilings,  the  area  of  surfaces,  the  volumes  of  solids  or  vessels, 
the  amount  of  land  in  fields,  the  amount  of  plastering  in  a 
room,  the  amount  of  carpet  required  to  cover  a  floor,  etc., etc. 
These  measures  will  thus  become  actual  and  practical  realities, 
and  not  mereh*  a  lot  of  names  to  be  committed  to  memory. 

Measures  of  3[oney. — In  teaching  the  measures  of  Money, 
the  teacher  should  show  the  pupils  the  cent,  dime,  dollar, 
eagle,  etc.  Every  school  should  be  provided  with  a  collection 
of  coins  to  illustrate  the  subject.  There  should  be  specimens 
also  of  the  English  penny,  half-penny,t,he  shilling,  sixpoice, 
florin,   etc.      In  teaching   French  money,  there   should  be 


TEACHING   PRIMARY    ARITHMETIC.  375 

specimens  of  the  franc,  half-franc^  five  centimes  or  sou.  ten 
centimes  or  two  sous.  In  teaching  German  money  we  shoultl 
present  tathe  pupil  the  mark,  the  thaler,  the  groschen,  etc. 
The  tables  are  also  to  be  committed,  written  on  the  board, 
and  repeated. 

Jleasures  of  Weight. — In  teaching  the  table  of  Weights, 
the  pupils  should  be  shown  the  ditferent  weights, — the  ounct, 
the  pound,  etc., — ■  and  be  required  to  examine  and  handle  them 
until  they  are  entirely  familiar  with  them.  They  should  see 
and  handle  the  pennyweight,  the  ounce,  the  pound,  Troy; 
also  the  scruple,  dram,  ounce,  and  pound,  Apothecaries. 
There  should  be  a  pair  of  scales  in  the  school-room  to  weigh 
objects.  Pupils  should  also  be  required  to  "  heft"  diflerent 
objects,  as  a  book,  a  chair,  etc.,  to  learn  to  judge  of  the 
weight  of  objects.  The  tables  of  weight  should  be  studied 
and  committed.  We  should  also  have  specimens  of  the 
gram,  decagram,  and  kilogram. 

Measures  of  Length. — The  teacher  should  give  the  pupil 
definite  ideas  of  all  the  measures  of  length.  There  should  be 
the  foot  and  yard  rules,  divided  into  inches,  half-inches,  etc.. 
Have  the  length  of  a  rod  marked  on  the  wall  or  floor,  show 
the  pupils  the  distance  of  a  mile,  a  half-mile,  etc.  Have  a 
meter  properly  divided,  show  its  relation  to  the  3'ard,  and 
give  definite  ideas  of  the  decimeter,  centimeter,  etc.  Pupils 
should  also  be  drilled  in  estimating  the  length  of  objects,  dis- 
tances, heights  of  ceilings,  of  trees,  etc. 

MeasHves  of  Surface. — The  teacher  should  mark  on  the 
board  a  square  inch,  square  foot, and  square  yard,  to  show 
what  is  meant  by  these  surfaces,  and  also  to  give  definite 
ideas  of  them.  Show  also  the  reason  why  9  sq.  ft.  make  one 
square  yard,  and  144  sq.  in.  equal  a  square  foot.  Measure  o  f 
a  square  rod  out  in  the  field,  and  also  an  acre,  and  have  pupils 
judge  of  the  number  of  acres  in  a  field.  Have  pupils  remem- 
ber that  a  square  about  209  feet,  or  70  paces  on  a  side,  is  an 
acre.     Teach  the  surfaces  in  tlie  metric  system  in  the  same 


376  METHODS   OF   TEACHING, 

way.     Have  the  pupils  study  and  recite  the  table  of  square 
measure. 

Measures  of  Volume The  teacher  should  show  the  pupils 

a  cubic  inch  and  a  cubic  foot. ^  He  should  draw  them  and  also 
the  cubic  yard  upon  the  blackboard.  He  should  also,  as 
clearl}-  as  possible,  show  the  relation  of  them, — that  is,  that 
27  cu.  ft.  equal  a  cubic  yard^  and  1728  cu.  in.  make  a  cubic 
foot — by  a  figure  on  the  board,  or  by  blocks  prepared  for 
the  purpose.  Give  them  an  idea  of  a  cord  by  taking  a  lot 
of  little  sticks  4  inches  long,  and  making  a  pile  8  inches  long 
and  4  inches  high,  and  show  them  that  a  cord  contains  128 
cu.  ft.  To  give  them  an  idea  of  a  cord  foot^  measure  off  1 
inch  of  the  little  cord,  and  run  a  thin  stick  or  a  piece  of  wire 
down,  cutting  off  a  part  of  the  pile  1  inch  long,  which  will 
represent  a  cord  foot;  they  will  thus  see  that  8  cord  feet 
make  a  cord. 

Liquid  Measure. — In  teaching  Liquid  Measure,  have  the 
measures  in  the  school-room, — the  gill^  the  pitit,  the  quart^ 
and  the  gallon.  Show  them  by  actual  trial  that  4  gills  will  fill 
a  pint,  2  pints  a  quart,  etc.  Barrels  and  hogsheads  can  be 
seen  at  a  store.  We  should  also  have  samples  of  the  Apothe- 
caries' liquid  measures  in  the  school, — the  miiiim^fluidrachms, 
fluidounces,  etc, 

Dry  Measure. — In  teaching  Dry  Measure,  the  pint  and 
quart  at  least  should  be  in  the  school-room.  Have  the  pupils 
call  at  the  grocer's  to  see  the  peck  and  bushel,  or  examine 
these  measures  at  home,  if  their  parents  have  them.  They 
should  also  be  led  to  compare  the  liquid  quart  and  dry  quart, 
etc.  The  metric  system  of  measures  should  also  be  in  the 
public  school,  and  the  pupils  be  drilled  on  them. 

Measures  of  Time. — Time  will  be  quite  easily  taught,  aa 
il:e  measures  are  in  such  constant  use.  We  should  begin 
with  the  day  as  the  most  natural  unit,  and  pass  to  the  other 
11  easures.  We  should  explain  how  nature  fixes  the  day,  and 
n  onth,  and  year,  and  give  the  meaning  of  these  terms.     By 


TEACHING   PRIMARY    ARITHMETIC.  377 

means  of  a  clock,  we  can  teach  the  number  of  hours  in  a  day, 
the  number  of  minutes  in  an  hour,  and  of  seconds  in  a  minute. 
The  number  of  days  in  each  month  is  best  taught  by  the 
stanza,  "  Thirty  days  hath  September,"  etc.  This  can  also  be 
remembered  by  the  hand,  the  fingers  representing  January-, 
March,  May,  etc.,  and  the  spaces  between  them  representing 
Februar}^  April,  June,  etc.  We  should  also  show  them  that 
tiie  calendar  begins  one  day  later  each  year,  and  two  days 
later  after  a  leap  year,  and  explain  the  reason  for  it.  When 
they  are  prepared  to  understand  it,  we  can  explain  the  reason 
for  leap  year,  etc. 

Circular  Measure. — In  teaching  Circular  Measure,  draw 
a  circle  on  the  board,  and  teach  the  different  parts — circum- 
ference, semi-circumference,  quadrant,  arc,  etc.  Then  explain 
the  division  into  360  equal  parts,  each  called  a  degree;  that 
the  semi-circumference  contains  180°,  and  the  quadrant  90°. 
Then  show  that  the  degrees  are  divided  into  60  equal  parts 
called  minutes,  and  the  minutes  into  60  equal  parts  called 
seconds.  Show  that  all  these  are  parts  of  the  circumference, 
that  they  are  not  of  a  fixed  length,  but  differ  in  size  with 
different  circles.  Call  attention  also  to  the  difference  between 
minutes  and  seconds  of  circular  measure  and  of  time  measure. 

A  drill  like  this  in  Denominate  Numbers  will  give  the 
pupils  definite  ideas  of  what  they  are  committing,  and  will 
make  these  tables  a  reality  to  them,  and  not  a  mere  collection 
of  abstract  names.  It  will  make  them  interesting  to  pupils 
and  much  more  easily'  remembered  than  when  taught  in  the 
usual  abstract  method  of  our  schools.  When  the  classes  are 
more  advanced,  the  many  interesting  facts  concerning  the 
tables — the  origin  of  their  names,  of  their  units,  etc. — may  be 
presented. 


CHAPTER    IV. 

TEACHING    MENTAL    ARITHMETIC. 

AFTER  completing  the  course  in  Primiirv  Arithmetic,  tin 
pupil  may  take  a  complete  course  of  Mental  Aritiinieti'- 
in  one  book,  and  a  complete  course  of  Written  Arithmetic  in 
another  book;  or  these  two  courses  ma}'  be  combined  in  one 
book,  as  the  teacher  prefers.  In  this  chapter  we  shall  speak 
of  the  Importance  of  Mental  Arithmetic,  its  Nature,  and  the 
Methods  of  Teaching  it. 

I.  Importance  of  Mental  Arithmetic. — Mental  Arithmetic 
has  become  one  of  the  most  popular  studies  of  tlie  public 
school;  in  many  places  it  has  been  the  idol  of  the  school- 
room around  which  have  centered  the  affections  of  teachers, 
pupils,  and  parents.  This  preference  is  not  a  mere  whim,  but 
is  founded  on  the  intiinsic  value  of  the  subject,  wliich  we 
shall  briefly  consider.  The  value  of  Mental  Arithmetic  is 
two-fold;  first,  as  a  mental  discipline,  and  second,  as  a  means 
of  cultivating  arithmetical  power. 

Mental  Discipline. — The  science  of  numbers  before  the 
introduction  of  Mental  Arithmetic,  was  far  less  useful  as  an 
educational  agenc}'  than  it  should  have  l)een.  Consisting 
mainly  of  rules  and  methods  of  operations,  without  leading 
the  pupil  to  see  the  reasons  for  these  operations,  it  failed  to 
give  that  high  degree  of  mental  discipline  which,  when  prop- 
erly taught,  it  is  so  well  adapted  to  atford.  By  the  introduc- 
tion of  Mental  Arithmetic  a  great  change  has  been  wrought 
in  this  respect;  the  spirit  of  analysis  has  entered  into  tlu; 
science;  and  now  the  science  of  numbers  presents  one  of  1  he- 
best,  if  not  the  very  best,  means  of  discipline  in  the  curricu- 
lum of  the  common  school.  . 

1.  Mental  Arithmetic  given  culture  to  the  reasuiiing  facul- 

(318) 


TEACHIXG    MENTAL    ARITHMETIC.  879 

ties.  No  study  in  the  scliool  equals,  surelj-  none  surpasses, 
Mental  Arithmetic  in  giving  exercise  and  development  to  the 
power  of  reasoning.  It  is  a  S3'stem  of  practical  logic ;  all  its 
processes  are  in  accordance  with  the  laws  of  thought ;  every 
step  is  a  judgment  direct  or  indirect;  and  the  entire  subject 
is  permeated  with  the  principles  of  logic.  Its  processes  are 
analytic,  and  it  thus  trains  the  mind  to  the  most  rigid  and 
severe  analysis.  Every  truth  is  bound  to  every  otlier  truth 
b}^  the  thread  of  related  thought;  and  the  mind  of  the  pupil 
becomes  habituated  to  following  a  chain  of  logically  connected 
judgments,  until  it  reaches  a  desired  conclusion.  It  is  thus 
clear  that  Mental  Arithmetic  must  be  very  valuable  in  sivincr 
culture  to  the  power  of  thought. 

2.  Mental  AiHthmetic  cultivates  the  power  of  attention. 
When  properly  taught,  no  study  compares  with  Mental 
Arithmetic  in  this  respect.  The  problem,  as  read  \>y  the 
teacher,  must  be  repeated  by  the  pupil,  each  number  is  to  be 
remembered  in  its  proper  place,  and  each  condition  properly 
related;  and  this  can  be  done  only  by  the  most  careful  atten- 
tion. Pupils  trained  in  this  way  acquire  the  abilit}'  to  repeat 
long  and  complicated  problems  with  ease  and  accuracy.  Such 
discipline  enables  them  to  fix  their  minds  upon  a  discourse 
and  reproduce  much  of  what  they  hear. 

3.  Mental  A  rithmetic  gives  culture  to  the  memory.  Memory 
dejJeiKls  upon  the  power  of  attention:  we  remember  that 
which  we  fix  in  the  mind  by  close  attention  ;  we  forget  that 
to  which  we  are  inattentive.  Few  persons,  after  hearing  a 
sermon  or  discourse,  can  tell  3'ou  anything  definite  concerning 
it,  because  they  are  careless  and  inattentive  listeners.  Any- 
thing that  trains  the  mind  to  habits  of  close  attention  tends 
to  give  strength  and  reliability  to  the  memory.  Mental 
Arithmetic,  therefore,  in  its  discipline  of  the  attention,  is  an 
important  means  of  training  the  memory  to  habits  of  readi- 
ness and  accuracy. 

4.  Mental  Arithmetic  cultivates  exactness  of  language.     It 


380  METHODS   OF   TEACHING. 

is  SO  rigidly  exact  in  its  processes  of  thought  that  it  requires 
corresponding  exactness  in  its  language.  The  right  word 
must  be  used  in  the  right  place,  or  the  reasoning  will  be  at 
fault.  The  language  of  Mental  Arithmetic  is  simple,  clear, 
and  precise;  and  the  mind,  becoming  habituated  to  such  forms 
of  expression,  will  naturally  incline  to  use  them  in  the  con- 
sideration of  subjects  not  mathematical. 

5.  Mental  Arithmetic  sharpens  and  strengthens  the  mind 
in  general.  The  s^-stcm  of  rigid  analysis  gives  point  and 
penetrating  power  to  the  mind,  and  enables  a  person  to  pierce 
a  subject  to  its  core  and  discern  its  elements.  In  this  respect, 
Mental  Arithmetic  is  a  sort  of  mental  whetstone  which  gives 
edo-e  and  keenness  to  the  mind.  Old  Robert  Recorde  called 
his  work  on  arithmetic  the  "Whetstone  of  Witte;"  had  he  lived 
until  the  era  of  Mental  Arithmetic,  he  would  have  seen  the 
full  meaning  of  his  words,  for  mental  arithmetic  is  indeed  a 
whetstone  of  wit,  a  sharpener  of  the  mental  faculties. 

It  also  strengthens  the  mind  as  well  as  sharpens  it.  The 
mind,  like  a  muscle,  grows  tough  by  hard  work;  we  toil  foi 
strength  in  study,  as  we  do  upon  the  playground  or  in  the 
o-ymnasium.  Mental  Arithmetic  is  a  mental  gymnastics ; 
through  it  the  mind  grows  strong  and  tough,  taking  hold  of 
difficulties  with  a  will,  laughing  at  obstacles,  and  rejoicing  in 
the  investigation  of  the  intricate  and  profound. 

6.  Mental  Arithmetic  prepares  a  pupil  for  extemporaneous 
speaking.  In  solving  a  problem  the  pupil  must  stand  up  be- 
fore his  class,  hold  the  conditions  of  his  problem  clearly  in  his 
mind,  and  proceed  to  develop  the  matter  under  consideration 
in  logical  forms  of  thought  and  expression.  This  is  precisely 
the  discipline  needed  to  make  a  good  extempore  speaker.  It 
also  tends  to  correct  the  habit  which  many  speakers  have  of 
talking  without  saying  much.  The  good  speaker  is  one  who 
utters  thought,  and  not  words  merely  ;  and  the  study  of  men- 
tal arithmetic  tends  to  cultivate  speakers  who  think  and  uttex 
thought. 


TEACHING   MENTAL   ARITHMETIC.  381 

Arithmetical  Power. — The  influence  of  Mental  Arithmetic 
has  been  no  less  marked  upon  the  science  of  arithmetic  itself. 
Consisting  heretofore  of  mechanical  methods  for  finding  re- 
sults, it  was  drj^,  uninteresting,  and  difficult.  Few  pupils 
attained  any  excellence  in  it ;  and  many  acquired  a  positive 
distaste  for  the  subject.  But  these  things  have  passed  away; 
a  new  era  has  dawned  upon  the  science  of  numbers  ;  a  "  royal 
road"  to  arithmetic  has  been  found ;  and  it  has  been  so 
graded  and  strewn  with  tlie  flowers  of  reason  and  philosophj' 
that  it  is  now  full  of  interest  and  pleasure  to  the  youthful 
learner.  The  agent  that  has  produced  this  change  is  the 
method  of  analysis  which  we  know  as  Mental  Arithmetic. 

1.  The  study  of  Mental  Arithmetic  gives  the  pupil  the  power 
of  independent  thought  in  arithmetic.  The  spirit  of  mental 
arithmetic  is  analysis.  It  is  not  merel}^  oral  arithmetic  ;  it  is 
analj'tical  arithmetic ;  and  in  this  consists  its  power.  Bj^  it 
pupils  become  able  to  investigate  for  themselves,  and  are  no 
longer  bound  down  to  the  dictation  of  rules.  "  The  rule  says 
so,"  is  no  longer  the  touchstone  of  the  science  or  the  key  to 
the  result ;  but  a  careful  comparison  of  the  conditions  of  the 
problem  will  enable  the  pupil  to  make  his  own  method  and 
derive  his  own  rule.  By  it  he  becomes,  not  a  mere  arithmet- 
ical machine,  h\it  an  original  thinker,  understanding  what  he 
does,  and  prepared  to  make  new  investigations  and  new  dis- 
coveries in  the  science.  If  we  were  obliged  to  choose  be- 
tween a  course  in  mental  and  one  in  written  arithmetic,  we 
should  take  a  complete  course  in  mental  in  connection  with 
the  fundamental  rules  of  written  arithmetic  ;  and  we  would 
turn  out  better-trained  thinkers  in  arithmetic  than  if  we  had 
drilled  them  in  the  usual  course  of  written  aritlimetic. 

2.  The  study  of  Mental  Arithmetic  is  an  excellent  prepara- 
tion for  Algebra.  Arithmetic  and  Algebra  are  intimately 
related,  algebra  being  a  kind  of  general  or  s^-mbolic  arithme- 
tic. The  analysis  of  mental  arithmetic  is  especially  similar 
to  the  elementary  reasoning  of  algebra,  the  main  ditference  be- 


382  METHODS   OF   TEACHIN-Q. 

ing  that  the  latter  employs  s^'mbols  which  render  it  more 
concise  and  general.  The  one  insensibly  glides  into  the  other 
by  the  snbstitution  of  a  symbol  for  a  word ;  and  it  is  thus 
evident  that  the  study  of  mental  arithmetic  is  a  most  valuable 
preparation  for  the  study  of  algebra. 

Its  Great  Value No  words  can  convey  a  full  appreciation 

of  the  importance  of  mental  arithmetic.  Onl}'  those  who 
experienced  the  transition  from  the  old  methods  to  the  new, 
can  full}'  realize  the  supreme  value  of  the  study.  Indeed, 
we  believe  that  the  method  of  mental  arithmetic  is  the  great- 
est improvement  in  modern  education ;  and  the  world  owes 
a  debt  of  gratitude  to  Warren  Col  burn,  its  author,  which  it 
can  never  pay.  Though  there  has  been  a  recent  reaction  in 
public  sentiment  against  the  subject,  we  believe  that  it  is 
merely  a  wave  of  opinion  and  cannot  be  permanent.  Mental 
ai-ithmetic  is  the  great  source  of  discipline  to  the  power  of 
thought  in  our  public  schools.  When  properly  taught,  it 
gives  quickness  of  perception,  keenness  of  insight,  toughness 
of  mental  fibre,  and  an  intellectual  power  and  grasp  that 
can  be  acquired  by  no  other  primary  study.  To  omit,  there- 
fore, a  thorough  course  in  mental  arithmetic  in  the  com- 
mon schools,  is  to  deprive  the  pupils  of  one  of  the  principal 
sources  of  thought  power. 

II.  Nature  of  Mental  Arithmetic. — In  order  to  teach 
Mental  Arithmetic  properly,  or  to  appreciate  its  value  as  an 
educational  agency,  its  nature  should  be  clearly  understood. 
It  is  a  popular  view  that  mental  arithmetic  is  merely  the 
working  of  problems  in  the  mind,  and  this  is  the  opinion  of 
many  who  oppose  it  as  a  distinct  study;  but  this  is  a  mistake, 
and  one  that  should  be  corrected.  The  genius  of  mental 
arithmetic  is  not  merel}'^  the  "  working  of  problems  in  the 
head,"  but  the  analytic  and  inductive  treatment  of  the  science 
of  numbers.  We  shall  attempt  in  a  few  words  to  explain  its 
nature. 

General  Nature. — A  system  of  Mental  Arithmetic  is  de- 


•  TEACHIXG   MENTAL   ARITHMETIC.  383 

veloped  upon  the  principles  of  Analysis  and  Induction.  The 
reasoning  j)rocesses  are  purely  analytical,  not  demonstrative  ; 
and  the  methods  of  operation  should  be  derived  from  these 
analyses  by  inference  or  induction.  Each  problem  is  resolved 
into  its  simple  elements,  and  the  relation  of  the  elements,  lead- 
ing to  the  desired  result,  determined  by  comparison.  When 
we  wish  to  derive  rules  to  apply  to  other  problems  of  the  same 
class,  we  notice  the  process  generated  by  the  analj'sis,  and 
generalize  this  process  into  a  rule. 

This  brief  statement  shows  the  philosophy  upon  which  a 
system  of  mental  arithmetic  is  founded.  It  is  purel}'  analytic 
and  inductive  ;  and  not  synthetic  and  deductive,  like  written 
arithmetic.  Anal^^sis  determines  the  process  in  fxny  particu- 
lar case,  and  Induction  derives  the  method  that  applies  to  all 
problems  of  the  same  class.  Analysis  and  Induction  are 
the  golden  ke^'s  which  unlock  the  various  complex  com- 
binations of  numl)ers ;  they  are  the  magic  wands  Avhose 
touch  unfolds  tiie  m3-sterious  and  beautiful  combinations  of 
numbers. 

Analysis. — Arithmetical  analysis  assumes  the  Unit  to  bo 
the  fundamental  idea  of  arithmetic,  and  comprehends  all  uum 
bers  and  their  relations  through  their  relation  to  the  unit.  It 
compares  numbers  and  the  effects  produced  b}'^  a  number  of 
equal  causes  through  their  relation  to  the  unit  or  the  effect 
of  a  single  cause.  It  comprehends  a  fraction  by  a  clear 
apprehension  of  the  relation  of  the  fractional  unit  to  the  inte- 
gral unit;  and  thus  develops  the  principles  and  methods  of 
fractions.  In  this  manner  the  whole  science  is  evolved,  pre- 
senting one  of  the  most  beautiful  examples  of  pure  logic  that 
can  be  found  in  any  science. 

The  simplicity  and  beauty  of  this  process  is  seen  in  the  fact 
that  the  unit  is  the  fundamental  idea  of  arithmetic.  Arith- 
metic begins  with  the  unit ;  all  numbers  arise  from  a  repeti- 
tion of  the  unit ;  fractions  have  their  origin  in  the  division  of 
tlie  unit.     Hence,  in  the  comparison  of  numbers  the  unit  nat- 


884  METHODS   OF   TEACHING. 

urally  becomes  the  basis  of  the  reasoning  process.  We  reason 
to  the  unit,  from  the  unit,  and  through  the  unit.  The  unit  is 
the  foundation  upon  which  we  build  ;  it  is  the  stepping-stone 
in  the  transition  of  thought ;  it  is  the  centre  around  which  the 
process  of  reasoning  revolves.  In  it  we  have  an  illustration 
of  the  general  principle  that  the  One  lies  at  the  basis  of  all 
tilings.  All  science  is  a  striving  after  the  One  which  con- 
tains  the  All ;  the  Cause  which  contains  the  phenomena,  the 
Law  which  contains  the  facts,  the  one  principle  that  binds  all 
variety  into  unit}'. 

Comparing  Integers. — In  applying  this  analysis  to  num- 
bers, we  have  three  cases:  First,  where  we  pass  from  the 
unit  to  a  number;  second,  where  we  pass  from  a  number  to 
the  unit;  and  third,  where  we  pass  from  a  number  to  a  number. 
In  the  first  and  second  cases,  the  transition  is  immediately 
made,  since  the  relation  is  immediately  apprehended,  being 
given  in  the  genesis  of  numbers.  In  the  other  case,  the  com- 
parison is  not  immediately  seen ;  it  must  therefore  be  made 
by  the  intermediate  comparison  of  each  to  the  unit.  That  is, 
in  passing  from  a  collection  to  a  collection,  or  from  one  num- 
ber to  another,  we  first  pass  to  the  unit  and  then  yrom  the 
unit. 

Thus,  take  the  problem,  "  If  4  apples  cost  12  cents,  what 
will  5  apples  cost?"  Here  the  cost  of  4  apples  is  the  known 
quantity,  the  cost  of  5  apples  is  the  unknown  quantity  ;  the 
object  is  to  determine  the  unknown  by  comparing  it  with  the 
known.  This  compai-ison  cannot  be  made  immediately,  since 
the  mind  does  not  readily  perceive  the  relation  between  fve 
and  four;  we  therefore  pass  from /our  to  one,  and  then  from 
one  to  five.  Thus  the  analysis  is :  "If /our  apples  cost  12 
cents,  one  apple  costs  \  of  12  cents,  or  3  cents;  and  if  one 
apple  costs  3  cents, /ue  apples  cost  5  times  3  cents,  or  15 
cents."  This  pi-oblem  also  illustrates  the  first  and  second 
cases  of  comparison. 

Comparing  Fractions. — With   Fractions   the   same    law 


TEACHING   MENTAL   ARITHMETIC.  386 

holds  as  with  Integers,  though  the  existence  of  fxoo  units, 
the  integral  unit  and  the  fractional  unit,  somewhat  compli- 
cates the  process.  There  are  three  distinct  cases  as  in 
integers:  (1)  yia.-ismgfvoma.n  integer  to  a  fraction;  (2)  passing 
from  a.  fraction  to  an  integer;  (3)  from  a  fraction  to  a  frac- 
tion. In  the  first  case,  we  pass  to  the  unit,  then  to  the 
fractional  unit, and  then  to  the  collection  of  fractional  units. 
In  the  second  case  we  pass  to  the  fractional  unit,  then  to  the 
integral  unit,  and  then  to  the  collection  of  integral  units.  In 
the  third  case  we  pass  to  the  fractional  unit,  then  to  the 
integral  unit,  then  to  the  other  fractional  unit,  then  to  the 
c:)llection  of  fractional  units. 

We  give  a  problem  of  the  third  class,  which  includes  also 
what  in  both  of  the  others  differs  from  the  case  of  integfers. 
Take  the  problem,  "If  f  of  a  j'ard  of  cloth  cost  8  cents, 
what  will  I  of  a  j-ard  cost?"  The  solution  is  as  follows:  "If 
2  tliirds  of  a  yard  cost  8  cents,  one-third  of  a  yard  costs  ^  of 
8  cents  or  4  cents,  and  three-thirds,  or  one  yard,  cost  3  times 
4  cents,  or  12  cents;  if  one  yard  cost  12  cents,  one-fourth  of 
a  yard  cost  |  of  12  cents,  or  3  cents,  and  three-fourths  of  a 
3'ard  cost  3  times  3  cents,  or  9  cents." 

Here  the  ol)iect  is  to  compare  |  with  §,  which  we  do  by  the 
intermediate  relations  of  the  units.     It 
is  as   if  one  stood  at  A  and  wished  to       .         A 
pass  to  E.     The  mind  cannot  step  di-    zFL  j-T    L.       t-Ha/' 
rectlv  over   from  A  to  E,  so   it   first         .s  ]-J- — i 

steps  two  steps  down  to  B,  then  three 

steps  up  to  C,  then /our  steps  down  to  D,  then  three  steps  up 
to  E. 

Application  of  Analysis. — These  analyses  represent  the 
spirit  of  Mental  Arithmetic.  Such  processes  of  reasoning  run 
through  the  entire  science.  The  subject  of  Fractions,  present- 
ing many  interesting  cases,  is  beautifully  unfolded  by  it.  It 
can  also  be  api^lied  to  prolilems  in  Simple  and  Compoimd 
Proportion  Partitive  Proportion,  Medial  Proportion,  etc., 
17 


386  METHODS    OF   TEACHING. 

giving  simple  and  elegant  solutions.  The  subject  of  Percent- 
age and  Interest  is  also  developed  by  analysis  with  great 
simplicity  and  elegance. 

Induction — The  office  of  Induction  in  Mental  Arithmetic 
is  to  derive  methods  of  operations  or  rules  from  the  analyses. 
The  object  of  these  methods  is  to  enable  us  to  reach  the  result 
directly  by  a  mech8.nical  operation,  instead  of  going  through 
the  process  of  analysis  ever}'  time  we  need  a  result.  Thus, 
suppose  we  wish  to  find  a  method  of  reducing  fractions  ^o 
lower  terms;  by  analysis  we  reduce  some  fraction  to  lower 
terms,  as  yV  equals  §;  and  then,  by  examining  the  process  or 
b}'  comparing  the  two  fractions,  we  can  derive  the  rule  for 
reducing  a  fraction  to  lower  terms.  The  same  thing  can  be 
done  for  all  the  many  cases  which  arise  in  fractions. 

Such  inferences  are  necessary  in  Mental  Arithmetic  if  we 
would  attain  any  methods  of  operation,  indei)endent  of  the 
analyses.  In  Written  Arithmetic  these  rules  ma}'  be  derived 
by  demonstration  ;  but  no  demonstration  is  appropriate  to  the 
spirit  of  Mental  Arithmetic.  To  introduce  demonstration 
in  Mt'utal  Arithmetic  would  destro}'  or  mar  its  anal3'tic 
spirit,  which  is  the  distinctive  characteristic  of  the  branch. 
B}'  the  use  of  induction,  the  analytical  spirit  of  the  science  is 
preserved,  while  it  becomes  practical  in  its  methods  and  con- 
cise in  its  operations. 

III.  Methods    of    Teaching    Mental   Arithmetic. — The 
course  in  Mental  Arithmetic  is  so  definitely  laid  down  in  our 
text-books,  and  the  methods  of  instruction  so  clearly  indicated, 
that  but  little  need  be  said  with  respect  to  methods  of  teach 
ing  the  subject.     Only  a  few  suggestions  will  be  presented. 

Pupils'  Preparation. — Pupils  in  preparing  their  lessons 
should  be  careful  to  go  through  the  form  of  analysis,  making 
the  clear  expression  of  the  reasoning  the  test  of  their  knowl- 
edge of  the  lesson.  To  perform  the  mechanical  operations 
necessary  to  attain  the  results  is  not  sufficient.  They  may 
aid  themselves,  however,  with  pencil  by  writing  out  the  solu- 


TEACHING   MENTAL  ARITHMETIC.  387 

tion,  where  it  is  long  and  complicated.  The  reducing  of  the 
solution  to  writing  requires  exactness  of  thought,  and  tlie 
seeing  of  the  analysis  will  aid  in  fixing  it  in  the  under- 
standing. 

Pupils  should  be  especially  careful  to  depend  upon  them- 
selves in  solving  the  problems.  The  habit  of  a  few  pupils  in 
the  class  working  out  the  more  difficult  problems  for  the 
others,  deprives  the  pupils  assisted  of  the  principal  benefit  of 
the  study.  A  pupil  should  never  be  allowed  to  take  the  solu- 
tion of  another  pupil  or  of  the  teacher  and  commit  it  to 
memory.  It  is  better  not  to  know  how  to  solve  a  problem  than 
to  solve  it  with  the  memor}'. 

The  Recitation. — At  the  recitation,  the  teacher  should 
read  the  problem  and  require  the  pupil  to  arise,  repeat  it,  and 
give  the  solution.  The  pupil  should  not  be  allowed  to  use 
the  book  during  recitation.  The  practice  of  some  teachers  of 
allowing  the  pupils  to  read  the  problems  and  solve  them  from 
the  book  is  a  needless  and  a  pernicious  one.  The  book  is  not 
needed  in  recitation  by  the  pupils ;  a  very  little  practice  will 
enable  them  to  reproduce  long  problems  and  hold  the  condi- 
tions in  the  mind  with  entire  ease.  More  than  half  the  benefit 
of  the  study  is  lost  when  the  pupils  solve  with  the  book  in 
their  hands. 

Pupils  may  be  required  to  wi'ite  out  their  solutions  on  paper 
or  on  the  blackboard.  This  is  especially  convenient  when 
the  class  is  large,  some  being  busy  writing  out  the  solutions, 
while  others  are  reciting  orally.  The  solutions  as  written 
should  be  not  merely  the  operations,  as  in  written  arithmetic, 
but  a  complete  anal^'sis  of  the  problem.  Where  the  solution 
makes  equational  thought  prominent,  the  form  of  writing  may 
approximate  that  used  in  algebra. 

Great  care  should  be  taken  that  the  language  of  the  solu- 
tion  be  concise  and  accurate.  The  pupil  should  be  required 
to  say  just  what  he  means.  The  teacher  should  not  accept 
his  "  0,  that's  what  I  meant,"  when  he  said  something  quite 


388  METHODS   OF  TEACHING. 

different.  The  singular  and  plural  should  be  used  as  accu- 
rately as  they  can  be  in  the  language  of  arithmetic.  We 
should  insist  also  upon  a  uniformity  of  tenses  in  a  solution, 
for  pupils  incline  to  get  their  tenses  very  much  mixed  in 
their  forms  of  statement. 

Methods  of  Hecitdtion. — There  are  several  different  meth- 
ods of  recitation  in  mental  arithmetic,  which  wc  shall  name 
and  describe.  Some  of  these  are  preferred  to  others,  but  all 
may  be  used  occasionally  with  advantage. 

Common  Method. — By  tliis  method  the  problems  are 
assigned  promiscuousl}-,  the  pupils  not  being  permitted  to 
use  the  book  during  recitation,  nor  retain  the  conditions  of 
the  problems  by  means  of  pencil  and  paper,  as  is  sometimes 
done.  The  pupil  selected  by  the  teacher  arises,  repeats  the 
problem,  and  gives  the  solution,  at  the  close  of  which  the  mis- 
takes that  may  have  been  made  should  be  corrected  by  the 
class  and  the  teacher. 

Silent  Mel/iod. — By  this  method  the  teacher  reads  a  prob- 
lem to  the  class,  and  then  the  pupils  silently  solve  it,  indicating 
the  completion  of  the  solution  by  the  upraised  hand.  After 
the  whole  class,  or  nearly  the  whole  class,  have  finished  the 
solution,  the  teacher  calls  upon  some  member,  who  arises,  re- 
peats the  problem,  and  gives  the  solution,  as  in  the  former 
method. 

In  this  method  the  whole  class  solves  every  problem,  thus 
securing  more  discipline  than  b}^  the  preceding  method.  It, 
however,  requires  more  time  than  the  former  method  ;  hence, 
not  so  many  problems  can  be  solved  at  a  recitation.  We 
prefer  the  first  method  for  advanced  pupils,  and  the  second, 
at  least  a  portion  of  the  time,  with  younger  pupils.  It  may 
also  be  used  now  and  then  for  variety. 

Chance  Assignment. — This  method  differs  from  the  first 
only  in  the  assignment  of  the  problems.  The  teacher  marks 
the  number  of  the  lesson  and  the  number  of  the  problem  upon 
small  pieces  of  paper,  which  the  pupils  take  out  of  a  box  passed 


TEACHING    MENTAL   ARITHMETIC.  389 

around  by  the  teacher  or  some  member  of  the  class.  The 
teacher,  then,  after  reading  a  problem,  instead  of  calling  upon 
a  pupil,  merely  gives  the  number  of  the  problem,  the  person 
having  the  number,  arising,  repeating,  and  solving  it.  By 
this  method  the  teacher  is  relieved  of  all  responsibility  with 
reference  to  the  hard  and  easy  problems ;  and  it  is  also  be- 
lieved that  better  attention  is  secured  with  it.  It  is  particu- 
larly adapted  to  reviews  and  public  examinations. 

Double  Assignment. — By  this  method  the  pupil  who  receives 
the  problem  from  the  teacher  arises,  repeats  it,  and  then  as- 
signs it  to  some  other  pupil  to  solve.  It  may  be  combined 
with  either  the  first  or  second  methods.  The  objects  of  this 
method  are  variety  and  interest. 

Method  by  Parts. — By  this  method,  different  parts  of  the 
same  problem  are  solved  by  different  pupils.  The  teacher 
reads  the  problem  and  assigns  it  to  a  pupil ;  and  after  he  has 
given  a  portion  of  the  solution,  another  is  called  upon,  who 
takes  up  the  solution  at  the  point  where  the  first  stops  ;  the 
second  is  succeeded  in  like  manner  by  a  third  ;  and  so  on 
until  the  solution  is  completed.  The  object  of  this  method  is 
to  secure  the  attentiou  of  the  whole  class,  which  it  does  very 
effectually.  It  is  particularly  suited  to  a  large  class  consist- 
ing of  young  pupils. 

Unnamed  Method. — By  this  method  the  teacher  reads  and 
assigns  several  problems  to  different  members  of  the  class  be- 
fore requiring  any  solutions,  after  which  those  who  have  re- 
ceived problems  are  called  upon  in  the  order  of  assignment 
for  their  solutions.  There  are  several  advantages  of  this 
method.  First,  the  pupil  having  some  time  to  think  of  the 
problem,  is  enabled  to  give  the  solution  with  more  promptness 
and  accuracy  ;  and,  second,  the  necessity  of  retaining  the 
numbers  and  their  relations  in  the  mind  for  several  minutes 
affords  a  good  discipline  to  the  memory. 

In  regard  to  these  methods,  the  first,  second,  and  third  are 
probably  the  best  for  the    usual  recitations ;  but  the  other 


390  METHODS   OF   TEACHING. 

methods  can  be  emploj-ed  very  profitably  with  younger  classes, 
or,  in  fact,  with  any  class,  to  relieve  monotony  and  awaken 
interest.  With  advanced  pupils  we  prefer  the  first  method, 
or  the  first  combined  with  the  third. 

Errors  to  be  Avoided. — There  is  a  large  number  of  errors 
to  which  pupils  in  every  section  of  the  country  are  liable,  a 
few  of  which  we  shall  mention.  There  are  many  words  which 
pupils  in  their  haste  mispronounce,  and  also  many  com- 
binations, which  by  a  careless  enunciation  make  ridiculous 
sense,  or  nonsense.  We  call  the  attention  to  a  few  of  them, 
suggesting  to  the  teacher  to  correct  these  and  others  he 
may  notice. 

''And''  is  often  called  "  an;''  ''for"  is  called  "fur;"  "of"  is 
pronounced  as  if  the  o  was  omitted  ;  words  commencing  with 
wh,  as  when,  which,  where,  etc.,  are  pronounced  as  if  spelled 
"wen,"  "wich,"  "were,"  etc.  "Gave  him"  is  called  "gavim;" 
"did  he"  is  called  "diddy;"  "had  he"  is  called  "haddy;"  "give 
him"  is  called  "givim;"  "give  her"  is  called  "giver ;"  "ivhich 
is"  is  often  changed  into  "  witches ;"  and  "how  many"  is  fre- 
quently transformed  into  "  hominy."  "  How  many  did  each 
earn"  is  often  rendered  "  hominy  did  e  churn." 

A  very  common  error,  and  one  exceedingly  ditficult  to  cor- 
rect, is  the  improper  use  of  the  and  are ;  as  in  the  following 
solution :  "  If  2  apples  cost  6  cents,  one  apple  will  cost  the  i 
of  6  cents,  which  are  3  cents."  Here  "the"  is  superfluous,  and 
"  are"  is  ungrammatical.  Pupils  are  so  determined  upon  tlie 
use  of  "the"  that  we  suggest  the  placing  of  a  "  big  the"  upon 
the  board,  and  allowing  the  class  to  point  to  it  every  time  the 
mistake  occurs. 

The  following  is  a  frequent  error:  "If  one  apple  cost  3  cents, 
for  12  cents  you  can  buy  as  many  apples  as  3  is  contained  in 
12,  which  are  4  times."  The  objections  are,  first,  3  is  not  con- 
tained any  apples  in  12  ;  secondly,  the  result  obtained  is  times, 
when  it  should  be  apples,  or  a  number  which  applies  to  both 
times  and  apples.     The  solution  should  be,  "  You  can  buy  as 


i 


TEACHING    MENTAL   ARITHMETIC.  391 

many  apples  for  12  cents  as  3  is  contained  times  in  12,  which 
are  4," 

With  regard  to  is  and  are,  it  is  not  easy  to  determine  which 
should  be  used  in  some  cases  in  Arithmetic.  It  may  be  that 
it  would  be  better  to  use  the  singular  form  always,  whether 
the  subject  is  an  abstract  or  a  concrete  number  ;  thus,  8  is  2 
times  4,  and  8  apples  is  2  times  4  apples.  But  since  custom 
sanctions  the  use  of"  are"  with  a  concrete  number  as  a  sub- 
ject, it  is  necessary  to  adhere  to  that  form.  There  is  some 
authority  for  using  "is"  in  the  "  Multiplication  Table,"  and 
it  would  be  at  least  convenient  if  the  singular  form  were  uni- 
versally adopted. 

Pupils  have  some  difficulty  in  knowing  how  to  read  such 
expressions  as  $|.  They  object  to  saying  "  |  dollars,''''  since 
there  are  not  enou<jfh  to  make  dollars,  and  they  also  object  to 
saying  "|  of  a  dollar^'''  since  there  are  only  3  thii'ds  in  a 
dollar.  The  second  is  undoul)tedly  a  correct  reading,  remem- 
bering that  %  is  an  imp7-oper  fraction. 

The  following  error  is  almost  universal :  "  2|  apples"  is  read 
•'  2  and  3  fourth  apples,''''  instead  of  "  2  and  S  fourths  apples.'''' 
The  expression  "  |  times''''  is  sanctioned  by  custom,  although 
it  is  not  strictly  in  accordance  with  grammatical  principles. 
It  is  rather  more  convenient  than  the  expression  \  of  a  time, 
although  evidently  a  violation  of  the  rules  of  language 

Conclusion — The  student  teachers  will  now  present  a  com- 
plete outline  of  the  subject  of  Mental  Arithmetic  under  the 
several  heads  :  1.  Fundamental  Rules ;  2.  Introduction  to 
Fractions  ;  3.  Treatment  of  Fractions  ;  4.  Denominate  Num- 
bers ;  5.  Proportion  ;  6.  Percentage  and  Interest ;  7.  Problems 
for  Analysis.  They  should  be  able  to  state  the  different  cases 
which  arise,  give  a  problem  illustrating  each  case,  and  present 
a  model  solution.  Let  the  teacher  ever  bear  in  mind  that  in 
teaching  mental  arithmetic,  he  should  aim  at  the  following 
objects  :  Accuracy  of  memory,  clearness  of  thought,  simplic- 
ity of  analysis,  and  conciseness  and  exactness  of  expression. 


CHAPTER  V. 

TEACHING  WRITTEN"   ARITHMETIC. 

IN  connection  with  the  course  in  Mental  Arithmetic,  there 
should  also  be  a  course  in  Written  Arithmetic.  This 
course  may  be  combined  in  the  same  book,  or  presented  in 
different  books,  as  the  teacher  prefers.  In  this  chaj>ter  we 
shall  speak  of  the  Nature  of  the  Course,  and  the  Methods  of 
Teaching  the  subject. 

I.  Nature  of  Written  Arithmetic. — Written  Arithmetic 
differs  from  Mental  Arithmetic  in  several  respects.  The  ob- 
ject of  Mental  Arithmetic  is  the  analysis  of  numbers;  the 
object  of  Written  Arithmetic  is  tho  attainment  of  skill  in  cal- 
culation. Written  Arithmetic  is  a  oalculus,  and  the  primary 
object  is  to  learn  to  work  with  the  Arabic  system.  The  second 
object  is  the  attainment  of  practical  methods  of  operation, 
and  the  acquisition  of  readiness  and  accuracy  in  the  use  of 
these  methods. 

Method  of  Trenttnent. — The  method  of  treatment  in  Writ- 
ten Arithmetic  should  be  more  deductive  than  that  of  Mental 
Arithmetic.  The  definitions  which  in  Primary  Arithmetic 
and  Mental  Arithmetic  are  given  in  the  inductive  form,  should 
here  be  presented  deductively.  In  the  previous  course  the 
rules  should  be  derived  by  induction  from  the  analyses  ;  but 
in  Written  Arithmetic  the  deductiA'e  method  must  also  be 
emplo^'ed.  Here  many  things  are  to  be  demonstrated,  and 
demonstration  is  a  deductive  form  of  reasoning.  While 
analysis  and  induction  are  often  used,  yet  the  spirit  of  the 
science  is  deductive  and  demonstrative  rather  than  anal3'tic 
and  inductive. 

Arrange tnent. — The  arrangement  of  the  subjects    in  the 

(392) 


TEACHING    WRITTEN    ARITHMETIC.  3f  3 

text-book  used  should  be  both  scientific  and  practical.  By  a 
scientific  arrangement  is  meant  such  an  order  as  the  logical  de- 
velopment of  the  subject  suggests.  By  a  practical  arrange- 
ment is  meant  such  an  order  as  is  best  adapted  to  the  wants 
of  pupils  in  pursuing  the  study.  A  merely  scientific  arrange- 
ment, however  satisfactory  to  the  accomplished  arithmetician, 
would  not  be  sufficiently  progressive  to  meet  tho  purpose  of 
instruction.  A  merely  practical  adaptation  of  the  easy  and 
difficult  parts  to  suit  the  young  learner,  mighl  completely 
Ignore  the  logical  relations  of  the  science,  and  thus  fail  to 
give  that  mental  discipline  which  the  logical  evolution  of  truth 
imparts.  These  two  methods  should  run  together;  the  work 
should  be  practically  adapted  to  instruction,  and  at  the  same 
time  the  philosophical  spirit  of  the  science  should  be  preserved. 

The  Gradation, — The  course  in  Written  Arithmetic 
should  be  carefully  adapted  to  the  ditferent  classes  of  pupils 
who  use  it.  It  should  be  simple  enough  for  30ung  pupils,  and 
yet  sufficiently  advanced  for  those  of  more  mature  minds. 
This  adaptation  may  be  accomplished  in  two  or  three  different 
ways.  The  first  part  of  the  work  should  be  very  simple,  the 
difficulties  gradually  increasing  as  the  pupil  acquires  strength 
and  culture.  The  teacher  ma}'  omit  certain  subjects  with 
elementary  classes  until  review,  or  until  the  pupil  is  pre- 
pared for  them.  Thus  the  more  difficult  matter  will  be  left 
for  the  pupil  until  he  will  have  become  somewhat  familiar  with 
the  easier  principles  and  rules,  and  will  have  gained  mental 
strength  to  cope  with  the  greater  difficulties.  Another  object 
gained  by  this  plan,  is  the  interest  that  new  matter  gives  to  a 
review. 

The  Reasoning. — In  Written  Arithmetic,  as  previously 
stated,  the  methods  of  reasoning  are  more  S3'nthetic  and  de- 
monstrative than  in  Mental  Arithmetic.  Thus,  many  subjects 
which  in  Mental  Arithmetic  we  treat  analj'tically,  in  Writ- 
ten Arithmetic  we  should  treat  by  demonstration;  as  may  be 
Been  in  Fractions,  Percentage,  etc.  Besides  this,  there  are 
17- 


391  METHODS  OF  TEACHING. 

many  subjects  in  Written  Arithmetic  which  are  purely  deduc- 
tive and  demonstrative  in  their  nature;  as  Proportion,  Pro- 
gressions, Evolution,  etc.  Hence,  the  pupil  will  be  required 
to  learn  demonstrative  reasoning  as  well  as  arithmetical 
analysis. 

The  Princijiles. — Arithmetic  as  a  science  involves,  and  as 
an  art  is  based  upon,  certain  principles;  and  the  most  import- 
ant of  these  should  be  distinctly  stated  and  clearly  demon- 
strated. The  form  of  statement  should  be  deductive;  nnd, 
when  not  too  difficult,  the  method  of  demonstration  should 
be  deductive  also.  In  other  cases  the  truth  may  be  shown 
inductively,  suggesting  to  tlie  pupil,  however,  that  it  is  sus- 
ceptible of  rigid  deductive  demonstration. 

Where  the  principles  are  essential  to  the  development  of  a 
subject,  the}'  should  be  given  at  the  beginning  of  the  treat- 
ment of  it ;  in  other  cases,  they  may  be  stated  at  the  close  of 
the  subject.  Thus,  in  Least  Common  Multiple,  Greatest  Com- 
mon Divisor,  Common  Fractions,  Proportion,  etc.,  the  princi- 
ples are  given  first,  and  the  development  based  upon  them;  in 
the  Fundamental  Rules,  etc.,  a  knowledge  of  some  of  the  prin- 
ciples not  being  essential  to  the  development  of  the  subjects 
themselves,  may  be  given  after  them. 

The  importance  of  principles  in  written  arithmetic  should 
not  be  overlooked.  Until  within  a  few  years,  American  text- 
books and  American  instruction  almost  completely  ignored 
the  principles  of  the  science,  making  arithmetic  to  consist 
entirely  in  the  solution  of  problems.  This  is  a  great  error, 
and  one  most  pernicious  in  mental  discipline.  Especially  is 
attention  to  principles  important  in  Normal  instruction, 
where  the  pupil  expects  to  teach  others.  No  matter  how  hard 
a  problem  he  can  soh  e,  if  he  cannot  give  neat  and  clear  expla- 
nations, he  is  unfit  to  be  an  instructor  of  others.  It  should  be 
rememben^d  also  that  a  clear  knowledge  of  the  principle  makes 
a  problem,  otherwise  difficult,  comparativeh'  eas}'. 

fhe  Problems. — Problems  are  of  two  kinds,  abstract  and 


TEACHING   WRITTEN   ARITHMETIC.  395 

concrete.  Abstract  problems  are  designed  to  illustrate  the 
principle,  or  fix  the  rule  in  the  mind.  They  serve  to  make 
pupils  read}'  and  accurate  in  the  mechanical  operations.  Such 
problems  should  be  suited  to  the  rule  the}'  illustrate  and  the 
capacit}'  of  the  pupil,  being  simple  at  first,  and  graduall}'  in- 
creasing in  difficult}'.  Concrete  problems  are  the  api)lication 
of  the  abstract  principles  to  something  that  either  does  or  may 
exist  in  actual  life.  These  problems  should  also  be  adapted 
to  the  subject  and  the  capacity  of  the  learner.  Simple  at  first, 
they  should  be  gradually  complicated  until  the  pupil  needs  to 
think  closely  to  unravel  the  complication  and  attain  the 
result. 

Number  of  Problems. — There  should  be  a  large  number  of 
problems  in  the  course  in  Written  Arithmetic.  Principles  and 
methods  are  fixed  in  the  mind  by  their  application,  and  prob- 
lems are  intended  for  such  application.  In  this  respect  there 
is  a  great  difference  between  the  French  and  English  works. 
The  French  have  many  i)rinciples  and  few  problems;  the  P]ng- 
lish  fewer  principles  and  more  problems.  The  true  method  is 
principles  and  problems,  enough  of  the  former,  the  more  the 
better  of  the  latter.  Especially  should  there  be  a  large  col- 
lection of  problems  under  the  fundamental  rules,  as  the  first 
object  in  the  study  of  arithmetic  is  to  acquire  skill  in  the 
mechanical  processes  of  adding,  multiplying,  etc. 

Variety  of  Problems. — Problems  should  be  so  varied  that 
the  solution  of  one  cannot  be  directly  and  mechanically 
applied  to  all  the  others  of  the  same  class.  This  is  an  impor- 
tant i)oint.  Many  teachers  who  condemn  the  faults  of  the  old 
schoolmasters  in  working  everything  by  rule,  fall  into  a  simi- 
lar error  by  requiring  pupils  to  solve  everything  by  "  model 
solufioyis.^"  To  give  a  pupil  a  solution  of  one  of  a  class  of 
problems,  and  then  have  him  apply  it  to  a  dozen  others  of  the 
same  class,  without  any  A'ariation  or  new  complication  of  the 
conditions,  so  as  to  require  original  thought  on  the  part 
of  the   pupil,  is  not    much  better  than  to  solve  by  the  old 


396  METHODS   OF   TEACHING. 

method  of  " /Ae  rule  says  so.^^  Problems  should,  therefore, 
be  varied  so  as  to  give  the  pupil  opportunity  for  original 
thought  and  investigation,  that  he  may  become  an  independ- 
ent reasoner  and  not  a  mental  parrot. 

Practical  Character. — The  practical  character  of  the  prob- 
lems should  be  a  prominent  feature  of  them.  They  should 
represent  the  actual  business  of  the  day,  and  not  the  scholar's 
idea  of  what  business  might  be.  The  problems  and  proces^'^es 
should  be  derived  froii.  actual  business  transactions,  and  the 
teacher  should  endeavor  to  make  this  one  of  the  leading  char- 
acteristics of  his  instruction. 

Solutions  and  Demonstrafions. — The  solutions  and  demon- 
strations should  be  simple  and  clear,  that  they  may  be  readily 
understood,  but  at  the  same  time  concise  and  logically  accu- 
rate. A  solution  may  be  too  concise  to  be  readily  inider- 
stood  ;  and  it  may  also  be  too  prolix,  the  idea  being  smoth- 
ered or  concealed  in  a  multiplicity  of  words.  Both  of  these 
errors  should  be  avoided.  There  is  a  language  of  arithmetical 
science,  simple,  clear,  and  concise,  as  appropriate  to  the  sci- 
ence of  numl)ers  as  the  language  of  geometry  is  to  the  science 
of  form.  This  language  is  the  natural  ex])ression  of  the  logi- 
cal evolution  of  the  subject,  and  should  be  employed  even  in 
the  most  elementary  ])rocesses  of  arithmetic.  The  teacher 
should  always  remember  that  the  highest  science  is  the  greatest 
simjilicity. 

The  Rules. — The  rules  of  arithmetic  are  statements  of  the 
methods  of  operation.  These  rules  should  be  expressed  in 
brief  and  simple  language,  and  in  a  form  easily  understood  by 
the  learner.  The  statement  should  not  be  too  general  in  its 
terms,  but  should  indicate  each  step  in  its  natural  order.  In 
most  cases  the  rule  should  be  derived  from  the  solution  of  a 
problem,  that  the  pupil  may  see  the  reason  for  it,  and  be  able 
to  dei'ive  it  himself,  as  an  inference  from  the  solution.  In  some 
cases  it  is  more  convenient  to  state  the  rule  first  and  then  de- 
monstrate it;  and  this  should  be  done  wherever  it  is  seen  to 


TEACinXG    WRITTEN    ARITHMETIC.  397 

be  preferable.  Youii^'  pupils  should  not  be  required  to  commit 
the  rule  to  memory,  ])ut  they  should  be  thoroughly  drilled  upon 
the  methods  of  openition.  Older  pupils  should  be  required  to 
describe  the  methods  of  operation,  and  the  study  of  the  rules  will 
aid  them  in  doing  this. 

Definitions. — The  definitions  should  be  clear,  concise,  and 
accurate.  There  are  two  methods  of  givinsr  definitions,  which 
are  distinguished  as  the  Inductive  and  Deductive  methods. 
By  the  Inductive  method  we  pass  from  the  idea  to  the  word  ; 
by  the  Deductive  method  we  pass  from  the  word  to  the  idea. 
Thus,  by  the  Inductive  method  we  would  say,  "The  process 
of  finding  the  sum  of  two  or  more  numbers  is  Addition;"  by 
the  Deductive  method  we  would  say,  "  Addition  is  the  process 
of  finding  the  sum  of  two  or  more  numbers."  In  the  course 
in  Priraaiy  and  Mental  Arithmetic,  the  Inductive  method  is 
preferred;  in  the  Written  Arithmetic,  the  Deductive  method 
should  be  used. 

Answers. — The  question  is  often  raised  whether  a  text- 
book on  Written  Arithmetic  should  contain  the  answers  to 
the  problems.  We  believe  that  most  of  the  problems  should 
have  no  answers  given  in  the  text-book.  In  case  of  any  pecu- 
liarity in  a  problem  by  which  pupils  would  be  liable  to  obtain 
an  incorrect  result,  the  correct  answer  should  be  given  ;  in 
other  cases  it  would  l>e  better  to  omit  them.  In  practical  life, 
our  problems  are  without  answers  ;  we  must  determine  the 
correct  results  for  ourselves.  Education  should  be  disciplin- 
ary for  life,  hence  the  pupil  should  learn  to  rely  upon  himself 
in  studying  his  text-book.  We  have  no  answers  in  Mental 
Arithmetic,  and  get  along  well  without  them;  could  we  not  do 
as  well  without  them  in  Written  Arithmetic? 

These  views,  however,  confiict  with  the  popular  view  and 
|)ractice.  Nearly  all  teaeluM's  prefer  having  answers  to  the 
problems  in  the  text-book  ;  and  with  elementary  classes  they 
may  be  of  some  practical  advantage,  to  both  pupil  and  teacher. 
Tliere  are  some  teachers,  however,  who  will  not  use  an  arith- 


398  METHODS    OF   TEACHING. 

meticwitli  answers;  and  several  authors  publish  two  editions 
of  their  works,  one  with  and  the  other  without  answers, 
so  as  to  meet  the  wants  of  all  in  this  respect, 

II.  Methods  of  Teaching  Written  Arithmetic.  As  con- 
ditions for  thorough  instruction  in  Written  Arithmetic,  each 
pupil  should  be  provided  with  an  arithmetic,  slate,  and  pencil. 
In  latter  times  book-slates  and  scribbling  paper  have  in  many 
places  superseded  slates,  and  are  in  some  respects  preferal)le 
to  the  old-fashioned  slate.  The  school-room  should  also  l;e 
furnished  with  a  blackboard  of  suitable  size  and  quality.  Tlie 
necessity  of  a  blackboard  in  the  school-room  is  imperative. 
No  good  teaching  can  be  done  without  it,  especially  in 
mathematics. 

Assif/iiiiient  of  the  Lesson. — The  lesson  should  be  assigned 
at  the  close  of  each  recitation,  that  the  pupil  may  have  time 
to  prepare  it  for  the  next  recitation.  In  assigning  the  lesson 
the  teacher  should  be  definite  as  to  place  and  extent,  stating 
just  where  a  lesson  begins  and  where  it  ends,  so  that  there 
can  be  no  doubt  about  it  by  the  pupil.  The  extent  of  the  les- 
son should  be  adapted  to  the  ability  of  the  class,  care  being 
taken  that  neither  too  much  nor  too  little  be  assigned.  Tiiis 
point  is  important,  for  if  too  little  be  given,  the  pupils  become 
lazy;  if  too  much,  they  will  become  discouraged  and  disgusted 
with  the  study.  Attention  should  also  be  called,  to' prominent 
points  or  unusual  difficulties,  that  they  may  receive  special 
attention  in  the  preparation  of  the  lesson. 

Preparation  of  the  Lesson. — In  the  preparation  of  the 
lesson  the  pupil  should  be  thrown,  as  far  as  possible,  upon  his 
own  resources.  The  teacher  should  give  him  no  assistance, 
or,  at  least,  very  little  ;  and  he  should  prevent,  as  far  as  possi- 
sible,  his  obtaining  any  from  other  memljers  of  the  class  or  the 
more  advanced  pupils.  The  habit  of  running  to  the  teacher 
with  every  little  difficulty  is  a  most  pernicious  one,  and  de- 
structive of  invigorating  mental  discipline.  Independence  of 
thought  and  bold  self-reliance  are  indispensable  traits  of  man 


TEACHING    WRITTEN    ARITHMETIC.  899 

hood,  and  should  be  cultivated  in  the  studies  of  youth,  and 
especially  in  the  study  of  mathematics,  which  is  particular!} 
adapted  to  give  such  training. 

This  point  cannot  be  too  stronglj'  urged  ;  its  neglect  has 
been  productive  of  much  mischief.  We  have  known  pupils 
who,  for  a  whole  session,  scarcel}'  ever  solved  a  problem  for 
themselves,  but  prepared  their  lessons  with  the  aid  of  otliei 
pupils.  At  other  times  they  have  obtained  notes  from  those 
who  had  previously'  passed  over  the  same  subject,  and  have 
used  these  notes  to  the  utter  neglect  of  self-thought.  It  is 
needless  to  sa}'  that  much  time  was  thrown  awa}^  and  that 
such  stud}'  is  worse  than  useless.  Let  the  pnpil,  in  the  pre- 
paration of  his  lesson,  depend  mainly  upon  himself;  and  what 
he  fails  to  get  out  in  this  way,  the  teacher  can  explain  to  him 
at  the  recitation. 

The  Recitation. — The  Recitation  is  the  great  instrument 
of  instruction.  In  it  the  teacher  comes  in  contact  with  the 
mind  of  the  pupil,  calls  out  its  energies  and  moulds  it  to  his 
will.  Mind  meets  mind  here — the  pupil's  mind  and  the 
teacher's  mind — thought  is  evolved,  and  mental  activity 
stimulated.  It  is  here  that  the  teacher  shows  his  power  as  a 
teacher,  rousing  up  dormant  faculties,  directing  mental  activ- 
ity, and  creating  interest  and  enthusiasm  in  that  which  was 
before  dry  and  repulsive. 

The  method  of  recitation  must  be  determined  by  the  several 
objects  to  be  attained.  These  objects,  briefly  stated,  aj-e:  1. 
To  find  out  what  the  pupil  knows  of  the  subject ;  2.  To  fix  the 
subject  clearly  in  the  mind  ;  3.  To  cultivate  the  power  of  accu- 
rate expression ;  4.  To  impart  instruction.  These  objects 
should  be  kept  clearly  before  the  mind  of  the  teacher  to  direct 
and  inspire  his  work. 

Method  of  Recitation. — The  lesson  being  prepared  and  the 
hour  of  recitation  having  arrived,  the  class  take  their  seats 
in  the  recitation-room  for  the  purpose  of  reciting.  The  teacher 
calls  the  roll  to  see  if  all  are  present,  and  then  proceeds  with 


400  METHODS   OF   TEACHING. 

the   recitation,  the   most   important  points  of  which  will  be 
briefly  specified. 

Preparation  of  the  Blackboard. — The  first  step  is  the  prepa- 
ration of  the  blackboard.  The  teacher  saj-s,  "  Prepare  the 
board,"  and  the  pupils  arise  and  pass  orderly  to  the  board, 
erase  what  work  there  may  be  on  it,  and  then  divide  it  into 
equal  spaces  hy  vertical  lines,  each  pupil  drawing  a  line  to  his 
right,  and  writing  his  name  at  the  upper  part  of  the  space. 
This  done,  as  quietly  as  possible,  the  pupils  turn  and  stand 
with  their  backs  to  the  board,  and  face  towards  the  teaclier. 

As.ngn7nent  of  Problems. — The  next  step  is  the  assignment 
of  problems.  With  young  classes  the  same  problem  should 
be  assigned  to  all  the  pupils,  or  at  least  one  problem  to  four 
or  five  pupils  ;  with  advanced  classes  each  pupil  should  receive 
a  different  problem.  If  the  class  is  not  too  large,  the  problem 
should  be  read  by  the  teacher,  and  the  pupil  be  required  to 
copy  the  conditions  as  he  reads.  When  the  class  is  large,  the 
pupils,  or  at  least  a  part  of  them,  may  be  permitted  to  copy 
the  problem  assigned  from  the  book.  They  should  be  required, 
however,  to  close  their  books  as  soon  as  the  conditions  are 
written. 

Writiug  the  Problem. — The  next  step,  or  one  co-ordinate 
with  the  above,  is  the  copying  of  the  problem  upon  the  board. 
Wlien  the  problem  is  abstract,  merely  requiring  an  operation 
upon  abstract  numbers,  the  pupil  will  copy  such  numbers  as 
the  teacher  reads.  If  the  problem  is  concrete,  involving  sev- 
eral cbnditions,  the  pupil  should  be  required  to  mark  the 
conditions  by  a  sort  of  short-hand  or  abbreviated  process 
which  he  can  write  rapidly,  and  which  will  be  readily  under- 
stood. He  should  also  write  the  page  and  number  of  the 
problem  at  the  upper  part  of  his  space,  so  that  the  teacher  may 
readily  refer  to  the  problem  in  the  text-book. 

Working  the  Problem. — The  next  step  is  the  working  of  the 
problem  upon  the  board.  In  this  the  pupil  should  practice 
neatness  and  exactness.     The  figures  should  be  plainly  and 


TEACHING   WRITTEN    ARITHMETIC.  401 

neatly  made.  The  lines  drawn  beneath  any  part  of  the  work 
should  be  straight  and  horizontal.  The  work  should  srener- 
alh'  be  written  in  the  form  which  a  person  would  employ  in 
actual  calculation.  It  may  sometimes  be  written  in  an  ana- 
lytic form,  the  operations  and  general  form  of  solution  being 
indicated  by  the  form  of  writing.  The  pupil  should  be  exact 
in  such  expressions,  and  not  write  one  thing  and  mean  another. 
Ever}'  point,  symbol,  etc.,  should  be  written  in  its  proper 
l)lace,  the  teacher  not  being  satisfied  by  the  pupil's  saying  he 
meant  so  and  so,  when  he  had  written  something  else,  or 
neglected  writing  some  essential  part.  Having  completed  the 
solution  of  the  problem,  the  pupil  should  take  his  seat  and 
retain  it  until  called   upon  by  the  teacher  for  his  explanation. 

roitition  at  the  Board. — In  reciting,  the  pupil  should  stand 
in  an  erect  and  easy  attitude,  with  the  pointer  in  one  hand  and 
the  other  hanging  down  by  the  side.  His  side,  and  not  his 
face,  should  be  turned  towards  the  board,  so  that  he  can  see 
both  the  solution  and  the  teacher.  The  teacher  should  be 
particular  upon  these  points,  allowing  no  awkwardness  or 
clownishness  of  attitude,  but  endeavoring  to  cultivate  an 
easy  and  graceful  carriage.  At  West  Point,  one  of  the 
best  mathematical  schools  in  the  country,  they  are  ver}' 
particular  upon  such  points  as  these,  and  the  effect  of  it  is 
seen  in  the  progress  and  attainments  of  the  pupils. 

Explanation. — The  explanation  of  the  problem  should  be 
given  in  a  full  and  natural  tone  of  voice,  with  great  care  in  re- 
spect to  clearness  of  thought,  accuracy  of  expression,  and  dis- 
tinctness of  enunciation.  Those  who  speak  too  low  should 
be  encouraged  to  speak  louder;  and  those  who  speak  in  a  loud 
and  declamatory-  style  should  be  taught  to  speak  in  a  lower 
and  more  natural  tone.  If  the  form  of  solution  is  analytical, 
each  point  should  be  clearlj^  stated  as  it  follows  a  preceding 
one,  care  being  taken  that  the  whole  chain  of  anahsis  be 
kept  complete.  If  the  solut^ion  is  deductive,  the  different 
steps  being  based  upon  principles  previousl}'^  explained,  these 


402  METHODS    OF   TEACHIXQ. 

principles  should  be  referred  to  in  their  proi)er  order  and  eon 
nection.     The  exphination  should  be  clear  and   full   in  all  its 
parts,  and  complete  as  a  logical  whole. 

Crificifyyns. — The  pupils  who  are  not  engaged  at  the  boaiil 
should  be  rei[uired  to  observe  closeh'  each  explanation,  notii- 
ing  carefully  all  mistakes  in  solution,  expression,  etc.  At 
the  close  of  the  solution,  the  class  should  be  called  upon  fni 
correction  of  erroi*s,  suggestion  of  improvements,  etc.  The 
character  of  the  solution,  whether  incorrect,  too  long,  or  no' 
surticiently  clear,  tlie  form  of  statement  upon  the  board,  po-^i 
tion  at  the  board,  st^le  of  expression,  etc.,  are  all  legitimal*' 
subjects  of  criticism.  After  the  pujjils  have  given  their  criti- 
cisms, the  teacher  should  present  any  other  suggestions  or 
corrections  which  may  be  required.  At  the  close  of  such 
criticisms,  the  pupil  \vho  explained  will  erase  his  work  upiui 
the  board,  and  receive  another  problem,  or  take  his  seat,  ami 
the  next  pupil  jiroceed  to  explain. 

Teacher's  Exftlaiuttiou. — It  is  often  necessary  for  the 
teacher  to  cx|)lain  some  principle  or  problem  to  the  class  ;  the 
proper  time  of  doing  this  will  be  suggested  by  circumstances. 
A  principle  that  several  meraViers  of  the  class  do  not  un<ler- 
stand,  and  which  is  essential  to  the  lesson  to  lie  recited,  should 
be  ex})lained  at  the  beginning  of  the  recitation.  A  ditlieult 
problem  should  not  be  explained  by  the  teacher  until  the 
class  have  tested  their  strength  with  it.  It  is  better  to  leave 
it  for  a  week  or  two,  to  see  if  the  class  cannot  solve  it  with- 
out assistance.  A  spirit  of  this  kind  can  lie  cultivated  so 
that  pupils  will  not  be  willing  to  have  the  teacher  explain  a 
[)roblem  until  they  have  assui-ed  themselves,  by  severe  labor, 
that  it  is  beyond  their  powers.  Assistance  in  this  respect  is 
often  better  given  by  suggestion  than  by  full  explanation. 
This  leaves  the  victory  partly  theirs,  and  affords  at  least  a 
partial  satisfaction  of  a  triumph. 

Neiv  Matter. — For  the  purpose  of  exciting  a  deeper  in- 
terest in  the  subject,  the  teacher  should   occasionally  intro- 


TEACHING   WRITTEN    ARITHMETIC.  403 

dace  new  matter  adapted  to  the  comprehension  of  the  class. 
This  ma3^  be  done  at  the  latter  part  of  the  recitation  hour,  oi 
he  may  occasionally  occupy  the  whole  period  in  a  lecture 
upon  the  subject.  This  will  give  enlarged  views  of  the  sub- 
ject, and  awaken  the  desire  of  going  beyond  the  limits  of 
the  text-book  used.  With  classes  sufficiently'  advanced,  a 
philosophical  discussion  of  the  subject,  showing  its  logical 
evolution  from  a  few  fundamental  ideas,  the  relation  of  the 
difterent  parts  to  each  other,  the  natural  transition  from 
Arithmetic  to  Algebra,  the  historical  development  of  some 
subject,  etc.,  will  be  instructive  and  interesting. 

Jteviews. — We  recommend  regular  reviews.  With  the 
younger  classes,  where  they  are  learning  merely  the  mechani- 
cal part,  they  need  not  be  so  frequent ;  but  with  other  classes 
we  suggest  a  review  at  the  close  of  each  week.  In  this  review, 
less  attention  may  be  given  to  the  problems,  and  more  to  defi- 
nitions and  principles.  We  should  have  pupils  write  analj'ti- 
cal  outlines  of  the  week's  work,  embracing  the  definitions, 
principles,  different  cases  under  each  subject,  etc.,  in  their 
logical  order.  Tliis  will  give  a  comprehensive  idea  of  the 
subject  as  a  whole,  and  exhibit  the  logical  relation  of  the  parts 
to  each  other. 

With  these  suggestions,  we  close  the  subject  of  arithmetical 
instruction,  trusting  that  teachers  may  realize  the  full  impor- 
tance of  the  stud}',  and  ma}'  not  only  develop  in  their  pupils 
the  power  of  accurate  and  skillful  computation,  but  train  them 
to  logical  habits  of  thought  and  to  a  full  appreciation  of  the 
beautiful  science  of  numbers. 


CHAPTER  VI. 

TEACHING   GEOMETRY. 

GEOMETRY  is  the  science  of  Extension.  Extension  is 
possible  only  in  space ;  hence  geometry  may  also  be 
(ielinecl  as  the  science  of  Space.  It  investigates  the  propei'- 
ties  and  relations  of  the  ditferent  figures  that  are  possible  in 
space.  These  figures  have  form  ;  hence  geometry'  treats  of 
the  forms  of  space,  and  has  been  defined  as  the  science  of 
Form. 

Form  is  of  two  kinds,  Pure  Form  and  Real  Form.  Pure 
Foi'm  is  a  portion  of  space  limited  in  thought,  but  not  filled 
with  content.  Real  Form  is  a  portion  of  space  filled  with 
some  material  content.  The  science  of  geometry  treats  of  Pure 
Form;  but  its  principles  may  be  applied  to  Real  Form. 

The  terra  Geometry-  is  derived  from  ge,  the  earth,  and  me- 
tron,  a  measure ;  and  means  literally  a  measuring  of  the 
earth,  being  equivalent  to  our  term,  land  sun-eying.  It  does 
not  appear,  however,  that  it  ever  had  simpl}'  this  significance. 
As  far  back  as  we  can  trace  the  science,  there  seems  to  have 
been  a  body  of  truths  designated  b}'  this  terra.  Indeed,  sorae 
of  the  principles  of  geometry  must  have  been  known  from  the 
very  beginning  of  history. 

Nature  of  Geometry. — Georaetry  is  the  science  of  Form. 
Its  subject-matter  is  lines,  surfaces,  volumes,  and  angles. 
These  general  conceptions  contain  many  special  forms ;  the 
description  of  these  forms  gives  rise  to  the  definitions  of  ge- 
ometr3\  When  we  consider  these  special  forms  of  quantity, 
as  well  as  quantity  itself,  we  perceive  some  truths  concerning 
them  that  are  self-e^^dent,  that  must  be  true,  since  they  can- 

(404) 


TEACHING   GEOMETRY.  405 

not  be  conceived  as  untrue.  These  self-evident  truths  are 
called  the  axioms  of  geometry. 

The  science  of  geometry  begins  with  these  primary  ideas 
of  space,  and  the  self-evident  truths  arising  out  of  them,  and 
from  these,  as  a  basis,  rises  to  the  higher  truths  by  a  process 
of  reasoning.  The  axioms  and  definitions  are,  therefore,  said 
to  be  the  basis  of  the  science  of  geometry.  The  definitions 
present  the  subjects  upon  which  we  reason ;  the  axioms  give 
some  of  the  truths  with  which  we  start,  and  also  the  laws 
which  guide  us  in  the  reasoning  process.  From  these  we 
trace  our  waj',  step  by  step,  to  the  loftiest  and  most  beautiful 
truths  of  the  science,  by  the  simple  process  of  comparison. 

Geometry  is  purely  a  deductive  science.  It  begins  with 
definite  ideas  giving  rise  to  stricth'  logical  definitions,  has  its 
fundamental  truths  or  axioms  given  by  Intuition,  and  with 
these  as  a  basis,  proceeds  by  the  logic  of  deduction  to  derive 
all  the  other  truths  of  the  science.  It  is  regarded  as  the  most 
perfect  model  of  a  deductive  science,  and  is  the  type  and 
model  of  all  science. 

Divisions  of  Geometry. — Geometry  is  divided  into  two 
branches  ;  Common  or  Synthetic  Geometry,  and  Higher  or 
Analytical  Geometry.  Common  or  Synthetic  Geometr}'  is 
that  which  compares  geometrical  quantities,  and  derives  their 
relations  through  the  ordinary  methods  of  reasoning.  It  is 
usualh'  restricted  to  the  use  of  the  straight  line  and  the  circle  ; 
and  includes  the  ordinary  plane  figures,  the  rectangular  solids, 
and  the  three  round  bodies,  the  cylinder,  the  cone,  and  the 
sphere.  Analytical  Geometry  is  a  method  of  applying  alge- 
braic analysis  to  the  investigation  of  the  forms  of  space.  It 
is  a  general  method  of  investigation  that  can  be  applied  to  all 
kinds  of  lines,  surfaces,  and  volumes. 

Origin  of  Geometry. — Geometry  is  generally  supposed  to 
have  had  its  origin  in  Egypt,  where  the  annual  overflowing  of 
the  Nile  obliterated  the  landmarks,  and  rendered  it  necessary 
to  have  recourse  to  mathematical  measurement  to  re-establish 


406  METHODS   OF   TEACHING. 

them.  This  origin  is  indicated  by  the  term  Geometry,  which, 
as  stated,  signifies  the  measurement  of  the  earth.  But,  what- 
ever may  have  been  the  origin  of  the  term,  the  natural  tend- 
ency of  the  human  mind  to  comi)are  things  in  respect  to 
their  forms  and  magnitudes  is  so  universal,  that  a  geometry 
more  or  less  perfect  must  have  existed  since  the  first  dawn  of 
civilization. 

Geometry,  originating  in  Eg^'pt,  is  supposed  to  have  been 
introduced  into  Greece  by  Thales,  who  lived  about  the  year 
650  B.  C.  Pythagoras,  who  lived  about  510  B,  C,  was  one 
of  the  earliest  Greek  geometers.  He  is  sujiposed  to  have  dis- 
covered the  following  principles:  1.  Only  three  plane  figures 
can  fill  up  the  space  about  a  point;  2.  The  sura  of  the  angles 
of  a  triangle  equals  two  right  angles ;  3.  The  celebrated  prop- 
osition of  the  square  on  the  hypothenuse.  Some  say  that  in 
honor  of  this  last  discoverv  he  sacrificed  one  hundred  oxen. 
Plutarch  says  but  one  ox ;  and  Cicero  doubts  even  that,  as  it 
was  in  opjiosition  to  his  doctrines  to  offer  bloody  sacrifices, 
and  suggests  that  they  may  have  been  images  made  of  flour 
or  clay. 

The  next  geometer  of  eminence  was  Anaxagoras,  who  com- 
posed a  treatise  on  the  quadrature  of  the  circle.  Plato,  the 
"  poetical  philosopher,"  delighted  in  the  science,  and  culti- 
vated it  with  great  success,  as  is  proved  by  his  simple  and 
elegant  solution  of  the  duplication  of  the  cube.  About  fifty 
years  after  the  time  of  Plato,  Euclid  collected  the  proposi- 
tions which  had  been  discovered  by  his  predecessors,  and 
formed  of  them  his  famous  '•'•Elements'''' — a  work  of  such  emi- 
nent excellence  that  by  many  it  is  regarded,  even  at  the  pres- 
ent day,  as  the  best  text-book  upon  the  subject  of  Elementary 
Geometry.  It  consists  of  fifteen  books,  thirteen  of  which  are 
known  to  have  been  written  b}'  Euclid;  but  the  fourteenth 
and  fifteenth  are  supposed  to  have  been  added  by  H^'psicles, 
of  Alexandria. 

Apollonius,  of  Perga,  about  250  years  B.  C,  composed  a 


TEACHING   GEOMETRY.  407 

treatise  on  Conic  Sections,  in  eight  books.  He  is  said  to  have 
given  them  their  names,  parabola,  ellipse,  and  hyperbola. 
About  the  same  time  flourished  Archimedes,  who  distin- 
guished himself  in  Geometry  by  the  discovery  of  the  beautiful 
relation  between  the  sphere  and  circumscribed  C3'linder.  He  is 
also  distinguislied  by  his  work  on  conoids  and  spheroids,  by 
his  discovery  of  the  exact  quadrature  of  the  jjarabola^  and  his 
very  ingenious  approximation  to  that  of  tlie  circle. 

Other  geometers  of  eminence  followed,  among  whom  the 
most  illustrious,  perhaps,  were  Pappus  and  Diophantus;  but 
the  Greek  geometry,  though  it  was  afterwards  enriched  by 
man}'  new  theorems,  may  be  said  to  have  reached  its  limits  in 
the  hands  of  Archimedes  and  Apollonius,  and  a  long  interval 
of  seventeen  centuries  elapsed  before  this  limit  was  passed. 
In  1637,  Descartes  published  his  Geometry,  which  contained 
the  first  systematic  application  of  algebra  to  the  solution  of 
geometrical  propositions.  Soon  after  this  followed  the  dis- 
covery of  the  infinitesimal  calculus  of  Leibnitz  and  Newton; 
and  from  that  time  to  the  present,  Geometry'  has  shared  in  the 
ireneral  progress  of  all  mathematical  sciences. 

Value  of  Geonietri/ Geometry  ranks  among  the  first  of 

all  studies  for  the  discipline  of  thought  power.  It  is  the  perfec- 
tion of  logic,  and  excels  in  training  the  mind  to  logical  habits 
of  thought.  In  this  respect  it  is  superior  to  the  study  of 
Logic  itself;  for  it  is  logic  embodied  in  the  science  of  form. 
While  logic  makes  us  familiar  with  the  principles  of  reasoning, 
geometr}-  trains  the  mind  to  the  habit  of  reasoning.  No  study 
is  so  well  adapted  to  make  close  and  acciirate  thinkers.  Euclid 
has  done  more  to  develop  the  logical  faculty  of  the  world  than 
any  book  ever  written.  It  has  been  the  inspiring  influence  of 
scientific  thought  for  ages,  and  is  one  of  the  corner-stones  of 
modern  civilization. 

Geometr}'  not  only  gives  mental  power,  but  is  a  test  of 
mental  power.  The  boy  who  cannot  readily  master  his  geome- 
tr}'  will  never  attain  to  much  in  the  domain  of  thought.     He 


408  METHODS   OF   TEACHING. 

may  have  a  fine  poetic  sense  that  will  make  a  writer  or  an 
orator ;  but  he  can  never  reach  anj-  eminence  in  scientific 
thought  or  philosophic  opinion.  All  the  great  geniuses  in  the 
realm  of  science,  as  far  as  is  known,  had  fine  mathematical 
abilities.  So  valuable  is  geometry  as  a  discipline  that  many 
lawyers  and  preacliers  review  tlieir  geometry  every  3'ear  in 
order  to  keep  the  mind  drilled  to  logical  habits  of  thinking. 

Geometry  is  of  value  in  all  the  sciences  and  arts.  "  It  is," 
says  Dr.  Hill,  "the  most  useful  of  all  the  sciences."  "No 
other  science,"  he  adds,  "  can  be  learned  unless  j-^ou  know 
geometry."  It  lies  at  the  basis  of  the  sciences  of  trigonome- 
try, analj'^tical  geometry,  and  the  transcendental  analysis, 
while  the  sublime  and  far-reaching  science  of  astronomy  could 
not  proceed  a  step  without  it.  Without  geometry,  the  sci- 
ences of  surveying  and  engineering,  with  all  their  practical 
results,  could  have  had  no  existence ;  and  the  mechanical  skill 
that  reared  the  p^-ramids  or  arched  the  dome  of  St.  Peter's 
would  have  been  impossible. 

Things  to  be  Taught. — The  things  to  be  taught  in  geome- 
try are  two-fold ;  Geometrical  Ideas  and  Geometrical  Truths. 
The  Geometrical  Ideas  include  the  various  elements  ;  as  lines, 
surfaces,  volumes,  and  angles.  These  embrace  all  the  differ- 
ent figures,  triangles,  quadrilaterals,  the  circle,  polj'edrons, 
cylinders,  cones,  and  the  sphere.  The  Truths  of  geometry 
are  the  Axioms  and  Theorems,  the  latter  of  which  can  be 
applied  to  the  solution  of  practical  problems. 

The  elements  of  geometry  are  simple  and  readily  under- 
stood by  children,  and  should  thus  be  presented  very  early 
in  the  course  of  instruction.  Many  of  the  truths  can  also  be 
easily  understood  and  may  be  taught  to  young  pupils.  The 
reasoning  of  geometry  requires  considerable  mental  develop- 
ment, and  cannot  be  understood  hy  children :  it  should  not, 
therefore,  as  a  rule,  be  presented,  before  pupils  are  twelve 
years  of  age.  We  shall,  therefore,  for  instruction,  divide  the 
subject  into  two  parts  ;  the  Elements  of  Geometry,  and  Geom- 
etrv  as  a  Scienp.p.. 


TEACHING  GEOMETRY.  409 

I.  The  Elements  of  Geometry. 

The  Elements  of  Geometr}-  include  all  such  instruction  as 
pupils  are  prepared  for  before  they  are  ready  to  take  up  the 
subject  as  a  science.  These  Elements  embrace  the  fundamen- 
tal ideas  and  truths  of  the  science.  The  Ideas  to  be  taught 
include  a  knowledge  of  all  the  figures  of  common  geometry, 
their  form,  nature,  parts,  and  the  names  of  the  figures  and 
their  parts.  The  Truths  to  be  presented  under  the  Elements 
include  some  of  the  axioms  and  some  of  the  simpler  theorems 
of  the  science. 

Importance. — The  importance  of  a  course  in  the  elements 
of  geometry  will  be  briefly  stated.  First,  a  knowledge  of 
geometry  is  adapted  to  the  young  mind.  One  of  the  earliest 
ideas  of  the  mind  is  that  of  form;  objects  present  themselves 
to  US  in  forms  ;  and  the  mind  naturally  passes  from  concrete 
form  to  the  conception  of  abstract  or  pure  form.  The  mental 
product  in  perception  is  the  picture  of  the  object,  a  picture 
of  its  form;  and  the  mind  is  thus  prepared,  from  the  begin- 
ning of  its  experience,  to  consider  the  subject  of  form. 

Second,  the  elenififs  of  geometry  should  be  taught  for  their 
practical  value.  P.il-  elements  of  geometry  enter  into  all  me- 
chanical operations,  and  are  of  use  in  nearly  everj-  occupation. 
To  omit  such  a  course,  as  our  common  schools  have  been  do- 
ing, is  to  send  out  into  the  avocations  of  life  i>eople  ignorant 
of  the  simplest  principles  of  mechanics.  Such  expressions 
heard  among  mechanics  as  a  "  long  square,"  a  "  slanting 
square,"  a  ''square  triangle,"  a  "long  circle,"  etc.,  show  the 
defects  of  our  common  schools  in  respect  to  this  branch.  The 
common  schools  are  fitting  persons  for  every  avocation ;  and 
they  should  give  pupils  at  least  the  fundamental  principles 
that  enter  into  so  many  of  the  practical  atfairs  of  life. 

Third,  inMrucfion  in  the  elements  of  geometry  lies  at  the 
basis  of  drawing.  The  simplest  figures  of  the  drawing  lesson 
are  the  geometrical  figures.  Drawing  should,  therefore,  begin 
18 


o 


410  METHODS   OF  TEACHING. 

in  geometry;  and  the  elements  of  geometry  may  be  made  a 
stepping-stone  to  the  introduction  of  drawing  into  the  public 
schools. 

Fourth,  lessons  in  geometry  will  be  of  value  in  school  disci- 
pline. Pupils  should  be  required  to  draw  figures  on  their 
slates,  and  this  will  give  employment  to  both  minds  and  fin- 
gers, and  keep  them  out  of  the  mischief  that  comes  from  idle- 
ness. In  this  manner  the  teacher  can  reduce  mischief  into 
geometry,  and  thus  interest  and  instruct  little  minds,  and 
keep  pupils  obedient  and  quiet,  because  they  are  busy  and 
happy. 

Principles  of  Teaching There  are  several  principles  that 

determine  the  order  and  methods  of  teaching  the  elements  of 
geometry,  which  we  state  briefl}'^ : 

1.  The  elements  of  geometry  should  precede  the  elements  of 
arithmetic.  It  has  been  customary  to  defer  geometry  until 
the  pupil  is  quite  familiar  with  the  elements  of  arithmetic, 
but  this  is  a  great  error  in  education.  The  elements  of 
geometry  are  much  easier  than  the  elements  of  arithmetic. 
The  ideas  of  number  are  much  more  abstract  than  the  ideas 
of  form.  The  child  of  four  years  of  age  can  acquire  but  a 
very  small  knowledge  of  arithmetic,  while  it  may  learn  to 
distinguish  and  name  nearly  all  the  ordinary  geometrical 
forms. 

2.  The  reasoning  of  geometry  should  follow  the  reasoning 
of  arithmetic.  Though  the  ideas  of  Geometry  are  simpler 
than  the  ideas  of  arithmetic,  the  reasoning  of  arithmetic  is 
much  simpler  than  the  reasoning  of  geometry.  The  former 
is  often  a  mere  succession  of  intuitive  judgments,  each  com- 
parison bearing  its  evidence  in  itself;  while  the  reasoning  of 
geometry  is  syllogistic,  depending  on  a  principle  of  inference. 
For  this  reason  the  reasoning  of  geometry  should  not  be  in- 
troduced until  the  pupil  has  made  considerable  progress  in 
arithmetic. 

3.  The  method  of  teaching  the  elements  of  geometry  should 


TEACHING   GEOMETRY.  411 

be  concrete.  The  pupil  should  see  the  forms,  rather  than  learn 
to  define  them.  Figures  cut  from  pasteboard,  models  made 
out  of  wood,  diagrams  on  the  board,  etc.,  should  be  exten- 
sively used  in  these  instructions.  Even  the  truths  should  be 
illustrated  or  presented  in  the  concrete,  rather  than  by  ab- 
stract demonstration. 

4.  The  method  of  teaching  should  be  inductive.  The  pupil 
should  be  led  to  the  idea  of  the  different  figures  and  to  the  dif- 
ferent truths.  He  should  be  led  to  see  the  distinguishing 
characteristics  of  figures,  the  reason  why  they  are  named  as 
the}''  are ;  and  in  many  cases  he  can  be  led  to  apply  the  appro- 
priate term  himself  by  appropriate  questions. 

I.  The  Geometrical  Ideas. — The  fundamental  Ideas  of  ge- 
ometry are  those  of  the  Line,  the  Surface,  and  the  Volume. 
These  elements  may  be  reached  in  two  ways,  analytically  or 
synthetically.  We  may  begin  with  the  idea  of  a  volume,  and 
pass  from  it  to  the  surface  and  line  as  elements  of  it;  or  we 
may  begin  with  a  point,  pass  to  the  idea  of  a  line,  from  the 
line  to  a  surface,  and  from  the  surface  to  a  volume.  The 
former  method  is  analytic ;  the  latter  is  synthetic. 

Analytic  Method, — We  ma}'^  present  the  elements  of  geo- 
metrical quantity  analytically  as  follows:  The  teacher  may 
take  some  regular  form,  as  a  box,  and  call  attention  to  it. 
He  then  takes  a  rule,  and  leads  the  pupils  to  see  that  it  can  be 
measured  in  three  directions ;  in  length,  breadth,  and  thick- 
ness. He  then  tells  them  that  these  measurements  are  called 
the  dimensions  of  the  box,  and  leads  them  to  see  that  it  has 
three  dimensions,  length,  breadth,  and  thickness. 

The  next  step  is  to  lead  them  to  call  it  a  solid.  He  leads 
them  to  call  water,  because  it  flows,  afltiid;  and  because  the 
hand  will  not  move  through  the  box,  as  through  the  water, 
we  call  the  box  a  solid.  He  then  leads  them  to  conceive  of 
the  form  of  the  box  in  space,  and  shows  that  the  hand  can 
move  through  this,  therefore,  this  form  is  not  a  solid ;  from 
which  they  may  see  that  the  better  term  is  volume.     They 


412  METHODS   OP   TEACHING. 

may  thus  be  led  to  conceive  of  form  in  pure  space ;  which  is 
the  ffeometrical  volume. 

The  next  step  is  to  teach  the  idea  of  a  surface.  The 
ceacher  leads  them  to  call  a  side  of  a  box  the  surface^  and  then 
measuring  it,  shows  that  a  surface  has  length  and  breadth. 
He  then  asks  how  far  they  can  see  into  the  surface,  and  thus 
leads  them  to  the  idea  that  it  has  no  thickness,  but  merely  the 
tico  dimensions,  length  and  breadth. 

He  then  leads  them  to  see  that  where  two  surfaces  meet, 
since  neither  has  anj'  thickness,  the  edge  will  have  no  l)readth 
nor  thickness,  but  merely  length ;  and  that  this  is  a  line.  In  a 
similar  manner,  he  may  show  that  the  end  of  a  line  has  no 
length,  breadth,  or  thickness,  and  is  called  a  point.  The  stu- 
dent-teacher may  be  required  to  put  this  description  into 
an  inductive  lesson. 

Synthetic  Method. — By  the  Synthetic  Method,  we  should 
have  a  pupil  conceive  a  point  in  space ;  then  cause  this 
point  to  move,  and  its  imaginary  pathway  would  be  a  line; 
then  conceive  this  line  to  move  in  the  direction  opposite  its 
lent^th,  and  it  will  form  a  surface ;  then  conceive  this  surface 
to  move  in  a  certain  waj',  and  its  motion  will  form  a  volume. 

This  method  is  a  legitimate  one  ;  the  principle  of  it  is 
employed  in  geometry  in  the  case  of  the  cylinder,  cone,  and 
sphere.  The  analytic  method  is  preferred,  however,  for  sev- 
eral reasons.  It  is  more  concrete  than  the  synthetic  method, 
as  it  begins  with  that  which  can  be  seen,  and  not  merely  con- 
ceived.  The  synthetic  method  begins  with  the  most  difficult 
geometrical  conception,  a  point,  which  has  no  dimensions,  but 
position  only. 

Lines. — The  pupil  has  now  the  general  idea  of  a  line;  the 
next  step  is  to  teach  the  three  kinds  of  lines,  the  straight, 
the  curved,  and  the  broken  line.  To  do  this,  take  a  small 
twig  to  represent  a  line ;  put  it  into  different  forms,  leading 
them  to  name  the  forms,  and  then  drawing  lines  to  represent 
these  forms,  have  them  appl}^  the  names  to  the  lines. 


TEACHING   GEOMETRY.  413 

Modd  Lesson. — Teacher.  "When  I  pull  this  stick  out  sti-aigliU-whafkmd 
of  a  stick  is  it?  Ptqyil.  A  straight  stick.  T.  If  I  draw  a  line  like  this 
on  the  board,  what  kind  of  a  line  is  it?  P.  A  straight  line.  T,  bend- 
ing the  stick,  says,  What  am  I  doing  to  the  stick?  P.  Bending  it. 
T.  When  I  have  bent  it,  what  kind  of  a  stick  is  it?  P.  A  bent  stick. 
T.  I  will  place  this  against  the  board  and  draw  a  line  of  the  same  shape; 
what  kind  of  a  line  is  it?  P.  A  bent  line.  T.  Very  well;  another  name 
for  this  line  is  curved  line  T.,  breaking  the  stick,  says,  What  am  I 
doing  with  the  stick?  P.  Breaking  it.  T.  When  I  have  broken  it,  what 
kind  of  a  stick  is  it?  P.  A.  broken  stick.  T.  I  will  place  it  against  the 
board,  and  draw  a  line  like  it  on  the  board;  what  kind  of  a  line  shall 
we  call  it  ?    P.  A  broken  line. 

The  Angle. — The  next  step  is  to  give  the  pupils  an  idea  of 
an  angle.,  and  of  the  several  kinds  of  angles.  This  maj'  be 
done  by  taking  some  object,  as  a  knife,  opening  it,  then  plac- 
ing two  straight  sticks  side  by  side,  and  making  an  opening 
like  an  angle,  leading  the  pupils  to  call  it  an  opening ;  and 
then  giving  the  correct  name,  have  the  pupils  define  an  angle. 
Lines  on  the  blackboard  may  also  be  used. 

Modd  Lesson. — Teacher,  taking  a  knife  and  opening  it,  asks.  What  am 
I  doing  ?  Pupils.  Opening  your  knife.  T.  The  space  between  the  blade 
and  the  handle  may  be  called  what?  P.  The  opening.  T.  I  will  lay 
two  sticks,  the  one  on  the  other,  and  open  them;  what  is  the  space  be- 
tween them  cjilled?  P.  An  opening.  T.  Yes,  that  is  right,  but  there  is 
another  name  for  it;  this  opening  is  called  an  angle.  T.  What  then  is 
an  angle?  P.  An  angle  is  the  opening  beticeen  two  lines.  The  teacher 
will  then  make  angles  and  require  the  pupils  to  make  angles  on  the  board. 

Kinds  of  Angles. — The  teacher  will  then  lead  the  pupils  to 
notice  the  difierence  between  angles,  to  see  that  some  are  sharp 
and  others  blunt;  and  that  these  may  be  called  acute  and  ob- 
tuse. Then  lead  them  to  see  that  there  is  one  neither  sharp 
nor  blunt,  and  which,  like  a  boy  who  is  neither  too  sharp  nor 
too  blunt,  is  just  right,  and  may  therefore  be  called  a  right 
angle.     The  student-teacher  will  put  this  into  a  model  lesson. 

Parallels,  etc. — We  next  teach  j^orallel  lines,  oblique  lines, 
converging  lines,  diverging  lines,  perpendicular  lines,  and 
ho7-izontal  lines.  The  method  is  simple ;  the  student-teacher 
iLay  describe  it  and  give  a  model  lesson. 


414  METHODS   OF   TEACHING. 

The  Triangle. — To  teach  the  Triangle^  give  the  children 
some  little  sticks,  and  have  them  make  "little  pens"  with 
them.  Tell  them  to  make  a  pen  with  Jive  sticks,  then  with 
four,  then  with  three,  then  with  two;  and  thus  lead  them  to 
see  that  three  lines  is  the  least  number  that  will  enclose  a  sur- 
face. Then  call  attention  to  a  fiarure  made  with  three  lines : 
ask  how  man}^  angles  it  has;  lead  them  to  call  the  lines  sides; 
then  lead  them  to  call  it  a  '■'■  three-side,''''  and  then  a  ^Hhree- 
angle,''''  and  then  introduce  tri,  and  lead  to  the  name  tri- 
angle. 

Kinds  of  Triangles. — Then  lead  them  to  see  that  triangles 
differ,  and  that  the  different  kinds  can  be  named  from  their 
angles  and  their  sides.  Then  lead  them  to  name  the  right-an- 
gled triangle,  the  obtuse-angled  triangle,  and  the  acute-angled 
triangle.  Lead  also  to  the  different  kinds  of  triangles  with 
respect  to  their  sides,  and  give  them  the  names  equilateral, 
isosceles,  and  scalene.  Have  them  draw  them  on  the  board, 
and  drill  them  until  the}'  are  entirely  familiar  with  them. 
Teach  also  the  base  and  altitude  of  the  triangle.  The  student- 
teacher  will  give  an  inductive  lesson  on  the  triangle. 

The  Quadrilateral Have  pupils  make  a  four-sided  figure, 

lead  them  to  name  it  from  its  angles  a.  four-angle,  give  the 
word  quadra,  lead  to  quadrangle,  its  proper  name.  Then 
lead  them  to  name  it  from  its  sides  a  four-side;  introduce 
lateral  for  side,  and  quadra  for  four,  and  lead  to  quadri- 
lateral. Then  lead  them  to  discover  the  three  classes  of 
quadrilaterals;  and  give  the  names  parallelogram,  trapezoid, 
and  trapezium.  Then  lead  them  to  discover  the  several  kinds 
of  parallelograms ;  the  rectangle,  square,  rhombus,  and  rhom- 
boid. The  subject  will  admit  of  a  beautiful  inductive  devel- 
opment, which  the  student-teacher  will  give. 

J*olygons.^We  should  then  give  a  general  lesson  on  Fol;/- 
gons,  including  the  pentagon,  hexagon,  heptagon,  etc.  We 
should  teach  the  meaning  of  perimeter,  area,  regular  and 
irregular  polygons,  their  division  into  triangles,  etc. 


TEACHING   GEOMETRY.  415 

The  Circle. — We  should  next  teach  the  Circle^  including 
the  circumference^  semi-circumference,  quadrant^  arc,  diam- 
eter, radius,  chord,  sector,  segment,  tangent,  etc.  We  should 
show  pupils  how  to  construct  the  circle,  and  require  them  to 
draw  and  name  the  different  parts.  Attention  may  be  called 
to  the  difference  between  the  circle  and  the  circumference, 
which  are  often  confounded.  The  use  of  the  circumferent-L- 
in  measuring  angles  may  also  be  explained,  and  the  division 
of  the  circumference  into  degrees,  minutes,  and  seconds. 
Pupils  may  also  be  taught  to  inscribe  squares  in  circles,  and 
circles  in  squares,  etc.  The}'  ma^-  also  be  shown  how  to  in- 
scribe a  regular  hexagon  by  taking  the  radius  as  a  side ;  and 
also  how  to  form  an  inscribed  triangle  from  the  inscribed 
hexagon.  The  student-teacher  will  give  a  model  lesson  ou 
the  circle. 

Volumes. — Among  the  Volumes  we  should  first  teach  the 
cube,  the  pyramid,  the  cylinder,  the  cone,  and  the  sphere^ 
We  next  teach  the  prism,  and  the  different  kinds  of  prisms, 
named  from  the  form  of  the  bases.  We  should  next  teach  the 
oblique  and  right  pj'isms,  the  parallelopipedons,  rectangular 
parallelopipedons,  the  frustum  of  a  pyramid,  frustum  of  a 
cone,  etc.  We  should  have  models  of  these  different  volumes, 
and  also  draw  them  and  show  pupils  how  to  draw  them  on 
the  board. 

Round  Bodies. — We  ma}' then  give  a  more  detailed  lesson 
on  the  three  round  bodies,  the  Cylinder,  the  Co7ie,  and  the 
Sphere.  We  may  show  that  the  cylinder  can  be  generated  by 
the  revolution  of  a  rectangle ;  explain  which  is  the  base,  the 
altitude,  and  the  convex  surface.  We  may  show  how  a  cone 
can  be  generated  b}-  the  revolution  of  a  right-angled  triangle 
about  one  of  its  sides,  and  explain  the  6a.se,  altitude,  slant 
height,  and  convex  surface.  We  ma}'  show  how  a  sphere  can 
be  generated  by  the  revolution  of  a  semicircle  around  the 
diameter,  and  explain  the  diameter,  radius,  convex  surface, 
small  circles  of  the  sphere,  great  circles,  spherical  triangles, 
spherical  polygons,  the  lane,  etc. 


416  METHODS   OF   TEACHING. 

We  mention  in  detail  the  things  to  be  taught,  so  that  3  oung 
teachers  may  have  a  clear  conception  of  the  course  sugg  isted. 
They  should  be  prepared  on  the  subject  themselves,  and  then 
know  how  to  present  it  in  an  interesting  manner.  Let  the 
student  teacher  be  required  to  present  a  model  lesson  on  each 
one  of  the  figures. 

II.  The  Geometrical  Truths, — Children  maj'  also  learn 
many  of  the  truths  of  geometry  as  well  as  the  ideas.  The 
truths  of  ireometrv  are  of  two  kinds;  those  that  are  self-evi- 
dent,  called  axioms,  and  those  that  are  derived  by  demonstra- 
tions, called  theorems. 

Many  of  the  self-evident  truths  of  geometry  are  readily 
understood  by  young  pupils.  Many  of  the  theorems  may  be 
illustrated  or  presented  by  what  might  be  called  a  concrete 
demonstration.  An  abstract  or  logical  demonstration  of  them 
would  be  too  difficult  for  children,  and  nothing  of  the  kind 
should  be  attempted.  Some  of  the  other  truths  which  cannot 
be  illustrated  may  be  taken  on  faith ;  the  pupils  accepting 
them,  not  because  they  can  see  a  reason  for  them,  but  because 
the  teacher  tells  them  they  are  true. 

Self-evidetit  Truths. — Little  children  may  readily  be  led 
to  see  that  "A  straight  line  is  the  shortest  distance  from  one 
point  to  another."  Unite  two  points  with  a  straight  line,  a 
curved  line,  and  a  broken  line,  and  they  will  see  by  intuition 
that  the  straight  line  is  the  shortest  route.  To  make  it  inter- 
esting, have  them  suppose  three  little  boys  start  from  the 
same  point  to  travel  on  three  lines,  and  they  will  readily  see 
which  has  the  shortest  road  to  travel.  The  ancients  used  to 
say  that  a  donkey  knew  that  one  side  of  a  triangle  was 
shorter  than  the  sum  of  the  other  two  sides,  for  he  would  go 
straight  across  from  one  comer  of  a  field  to  the  other,  rather 
than  follow  the  two  sides  of  the  field. 

They  may  also  be  taught  to  see  that  "  two  right  angles  are 
equal  to  one  another."  Care  should  be  taken  that  they  see 
that  the  size  of  the  angle  depends  on  the  extent  of  the  open- 


TEACHING   GEOMETKY.  417 

ing,  and  not  on  the  length  of  the  sides.  They  may  also  read- 
ily see  that  "the  diameters  of  the  same  circle  are  all  equal;" 
that  "  the  radii  are  all  equal ;"  that  "the  radius  is  half  the 
diameter,"  etc.  In  fact,  they  may  be  taught  nearly  all  the 
geometrical  axioms.  The  student-teacher  will  present  the 
lesson. 

Truths  by  Concrete  Demonstration. — Many  of  the  truths 
of  geometry  can  be  taught  by  concrete  deniondrilion.  That 
is,  they  may  be  illustrated  in  such  a  way  that  pupils  can  be 
assured  of  their  truthfulness  without  depending  upon  the 
statement  of  the  book  or  the  teacher.  We  will  give  a  list  ol 
such  theorems,  and  suggestions  for  their  illustration. 

1.  If  one  straight  line  meet  another  straight  line^  the  sum 
of  the  two  adjacent  angles  equals  two  right  angles.  Take  two 
straight  sticks,  A  and  B  ;  place  the  end  of  A  near  the  middle 
of  B,  perpendicular  to  it ;  then  will  be  formed  two  right  an- 
gles. Then  incline  the  stick  A,  and  the  pupil  can  see  that  one 
angle  loses  what  the  other  gains,  and  that  they  both  just  fill 
up  the  space  of  two  right  angles,  and  hence  are  always  equal 
to  two  riarht  angles.     Illustrate  the  same  also  on  t-he  board. 

2.  All  the  angles  formed  on  one  side  of  a  straight  line  by 
drawing  lines  from  the  same  point,  are  equal  to  two  right 
angles.  This  can  be  shown  as  in  the  previous  theorem,  and 
the  pupil  may  illustrate  it  on  the  board. 

3.  The  sum  of  the  three  angles  of  a  plane  triangle  is  equal 
to  two  right  angles.  To  illustrate  this,  cut  out  a  triangle  from 
stiff  paper  of  any  form;-  then  cut  off  two  of  the  angles,  and 
place  one  on  each  side  of  the  third  angle,  and  it  will  be  found 
that  they  Just  fill  up  the  angular  space  of  two  right  angles. 

4.  If  two  triangles  have  two  sides  and  the  included  angle  of 
one  respectively  equal  to  two  sides  and  the  included  angle  of 
the  other,  the  two  triangles  are  equal.  To  show  this,  cut  out 
of  paper  a  triangle  of  any  shape  ;  then  mark  out  on  another 
piece  of  paper  two  sides  and  an  included  angle  equal  to  those 
of  the  given  triangle,  then  draw   a   straight  line  uniting  the 

18* 


418  METHODS   OF   TEACHING. 

extremities  of  the  sides,  cut  out  the  triangle,  and  compare 
them  b}'  placing  one  on  the  other,  and  it  will  be  found  that 
they  exactl}'  coincide. 

5.  The  area  of  a  r'ectangle  equals  the  number  of  units  in 
the  base  multiplied  by  the  number  of  units  in  the  altitude. 
Take  any  number  of  square  blocks,  as  foe,  and  pile  them  up 
in  three  rows  of  fve  each,  forming  a  rectangle.  The  whole 
surface  of  the  rectangle  is  formed  by  the  one  side  of  the  square 
blocks,  and  since  there  are  5  in  a  row,  and  3  rows,  there  are 
3  times  5,  or  15,  in  all;  hence  the  product  of  the  number  of 
units  in  the  base  multiplied  by  the  number  of  units  in  the 
height,  will  give  the  whole  number  of  square  units  in  the  sur- 
face.    Illustrate  it  also  on  the  blackboard. 

6.  The  area  of  a  parallelogram  is  equal  to  the  product  of 
the  base  and  altitude.  Cut  out  a  paper  parallelogram,  cut  off 
one  corner  vertically  across  ;  put  this  triangle  on  the  other 
end  of  the  parallelogram,  and  it  will  become  a  rectangle.  Now 
the  surface  of  this  rectangle  is  precisely  the  same  as  the  sur- 
face of  the  parallelogram,  and  its  base  and  altitude  are  the 
same.  But  the  area  of  this  rectangle  is  equal  to  the  product 
of  the  base  and  altitude  ;  hence  the  area  of  the  parallelogram 
is  equal  to  the  product  of  the  base  and  altitude. 

7.  The  area  of  a  triangle  equals  the  product  of  the  base  by 
half  the  altitude.  Cut  out  a  parallelogram;  then  divide  it 
into  two  triangles,  cutting  across  from  one  corner  to  the  other. 
These  two  triangles  are  equal,  and  hence  equal  to  one-half  of 
the  parallelogram,  and  hence  to  one-half  of  the  product  of  the 
base  multiplied  by  the  altitude. 

8.  The  area  of  a  trap)ezoid  is  equal  to  the  sum,  of  the  two 
parallel  sides  multiplied  by  half  the  altitude.  This  can  be 
shown  by  cutting  out  a  trapezoid,  dividing  it  into  two  tri- 
angles, showing  that  the  area  of  each  equals  its  base  into  one- 
half  of  its  altitude,  and  that  their  sum  will  be  the  sum  of  the 
two  bases  into  one-half  of  the  altitude. 

9.  The  square  on  the   hypothenuse  of  a  right-angled  tri- 


TEACUING    GEOMETRY.  419 

antfiti  is  equal  to  the  sum  of  the  squares  on  the  other  two  siaes 
Make  a  right-angled  triangle  on  tlie  board,  one  side  3  and  the 
other  side  4,  the  liypotheuuse  will  be  5;  construct  squares  on 
each,  and  divide  them  into  small  squares;  the  square  on  one 
side  will  co;  tain  9,  that  on  the  other  16,  and  that  on  the 
hj'pothenusi'  25;  and  25  we  see  is  the  sum  of  9  and  16.  Here 
we  see  that  '.he  squai-e  on  the  hypothenuse  is  equal  to  the  sum 
of  the  squa  es  on  the  other  two  sides. 

Many  otLer  truths  can  be  taught  in  this  way ;  and  such  a 
concrete  consideration  of  the  subject  will  be  a  valuable  prep- 
aration for  the  stud^'  of  the  subject  abstractl3'.  Let  the 
student-teacher  give  a  lesson  on  each  one  of  these,  using 
paper  and  the  blackboard. 

III.  TinJTHs  TO  BE  Taken  on  Faith. — We  should  teach  the 
pupils  of  the  common  school  some  truths  that  cannot  be  illus- 
trated to  them.  Such  truths  they  may  take  on  faith  ;  pupils 
believing  them  as  they  do  the  facts  of  geography  and  histoiy, 
because  the  teacher  states  them  as  true.  This  instruction 
may  extend  to  curves  not  treated  of  in  ordinary  geom- 
etry, including  the  Parabola,  the  Ellii)se,  the  Hyperbola,  the 
Cycloid,  the  Catenaiy,  etc. 

J/t  Ordinary  Geometry It  will  be  well  to  teach  the  more 

advanced  pupils  how  to  find  the  circumference  of  the  circle  by 
multipUjing  the  diameter  by  3.1416,  to  find  the  area  by  mitlti- 
plyiruj  the  circumference  by  half  [he  radius;  that  an  angle 
at  the  centre  is  measured  by  the  arc  included  between  its  sides: 
that  an  angle  at  the  circumference  is  measured  by  one-half 
the  arc  included  between  its  sides;  how  to  find  the  volume  of 
a  prism,  the  convex  surface  and  volume  of  a  cylinder,  the 
volume  and  convex  surface  of  a  pyramid  and  a  cone,  the  sur- 
face and  volume  of  a  sphere.  These  should  be  introduced  as 
they  are  prepared  for  them,  the  pupils  being  drilled  on  their 
application,  but  no  attempt  being  made  to  explain  the  reason 
for  them. 

Tlie  Parabola. — If  a  cone  be  cut  by  a  plane  parallel  to  its 


420  METUODS   OF   TEACHING, 

slanting  sides,  the  section  formed  is  a  beautiful  curve  called  a 
Parabola.  This  is  a  very  interesting  curve.  Every  stone  that 
a  little  bo3'  throws  at  an  object  forms  a  parabola  in  its  flight. 
In  a  snow-balling  match,  all  the  balls  form  parabolic  curves  ; 
and  in  a  battle,  shot  and  shell  go  hummingr  and  screechin2 
through  the  air  in  parabolic  arcs.  It  may  be  well  to  show 
that  the  area  of  a  section  of  this  curve  is  two-thirds  of  the  bane 
muHiplied  by  the  altitude.  This  area  may  be  compared  with 
the  area  of  a  rectangle  and  triangle  of  the  same  base  and  alti- 
tude.  The  method  of  constructing  a  parabola  should  also  be 
given. 

The  Ellipse. — If  a  cone  be  cut  by  a  plane  making  an  angle 
with  the  base  l.ess  than  tliat  made  by  the  side  of  the  cone,  the 
result  will  be  a  closed  curve  that  looks  like  a  circle  drawn  out. 
Such  a  curve  is  called  an  Ellipae.  This  curve  can  be  made 
by  driving  two  pins  in  a  board,  and  tying  a  string  at  each  end 
to  one  of  these  pins,  and  then  putting  a  pencil  point  inside 
the  string,  stretching  it  out  and  moving  it  round.  A  doubled 
string  passed  around  the  jjins  is  still  better.  The  two  points 
at  the  pins  are  called  the  foci  of  the  ellipse.  The  point  be- 
tween these  is  the  centre^  a  line  through  tlie  foci  is  called  the 
vxajor  axis  ;  and  a  line  perpendicular  to  this  throug'i  the  cen- 
tre is  the  minor  axis. 

The  ellipse  is  also  an  interesting  curve.  The  earth  in  its 
march  around  the  sun  follows  a  pathway  of  the  form  of  an 
ellipse,  the  sun  being  in  one  of  the  foci  of  the  elliptical  orbit. 
The  moon  moves  around  the  earth  in  an  ellipse,  and  all  the 
planets  and  satellites  move  in  the  same  curve.  To  find  the 
area  of  an  ellipse,  we  multiply  the  half  of  the  two  axes  toijcther, 
and  that  product  by  3.1416.  Another  interesting  fact  is  that 
if  we  had  a  mirror  in  the  form  of  an  ellipse,  a  light  placed  at 
one  focus  would  have  its  rays  all  reflected  in  the  other  focus; 
and  if  we  had  a  whispering  gallery  in  this  form,  a  whisper  at 
one  focus  would  be  distinctly  heard  at  the  other  focus, 

T/ie  Hyperbola. — If  a  cone  be  cut  by  a  plane  making  a 


TEACHING   GEOMETRY.  42] 

larger  angle  with  the  base  than  the  slanting  side  makes  with 
it,  the  curve  formed  is  an  Hyperbola.  If  we  tie  strings  at  dif- 
ferent points  of  a  horizontal  v.ire,  and  draw  them  all  through 
a  point  below  the  wire  and  cut  them  off  at  the  point,  when 
they  hang  down  straight  their  ends  will  form  an  hyperbola. 
If  we  tie  threads  to  each  link  of  a  hanging  chain,  and  cut  olf 
their  ends  in  a  level  line,  and  then  draw  the  chain  out  hori- 
zontal, the  lower  ends  of  the  threads  will  form  an  hyper- 
bola. There  are  many  interesting  truths  concerning  the 
hyperbola. 

The  Cycloid. — If  a  wagon  wheel  roll  on  a  level  floor,  a  nail 
in  the  tire  or  rim  will  make  a  series  of  curves,  each  called  a 
Cycloid.  A  boy  can  make  a  cycloid  by  fastening  a  pencil  to  a 
spool  and  rolling  the  spool  slowly  against  the  inside  of  the 
frame  of  his  slate.  There  are  several  interesting  properties  of 
the  cycloid. 

1.  The  height  of  the  cycloid  at  the  middle  is  equal  to  the 
diameter  of  the  wheel  or  circle  which  formed  it.  2.  The 
length  of  the  straight  line  joining  the  two  ends  of  the  curve, 
called  the  bane,  is  equal  to  the  circumference  of  the  generat- 
ino-  circle.  3.  The  leng^th  of  the  curve  is  four  times  the  diam- 
eter  of  the  generating  circle.  4.  The  area  of  the  curve  is  equal 
to  three  times  the  area  of  the  generating  circle.  When  the 
circle  is  at  the  middle  of  the  cycloid,  the  curious  looking 
three-cornered  figures  on  each  side  of  the  circle  are  each 
exactly  as  large  as  the  circle  itself. 

5.  If  a  cycloid  is  turned  upside  down,  a  ball  will  roll  down 
it  quicker  than  on  axvy  other  curve :  for  this  reason  the 
cycloid  is  called  the  curve  of  swiftest  descent.  If  a  hill  were 
hollowed  out  in  the  form  of  a  cycloid,  a  sled  would  run  down 
it  faster  than  if  it  were  of  any  other  shape. 

6.  Another  curious  property  is  that  if  several  balls  start  at 
different  points  on  the  curve  at  the  same  moment,  they  will  all 
reach  the  bottom  at  the  same  time ;  so  that  it  is  also  the  curve 
of  equal  descent. 


422  METHODS   OF   TEACHING. 

The  Catenari/. — When  a  chain  hangs  from  two  posts,  it 
makes  an  interesting  curve,  called  a  Catenary.  A  jumping 
rope,  a  clothes-line,  and  a  gate  chain,  all  hang  in  the  form  of 
a  catenary-.  The  curve  was  first  noticed  by  Galileo,  who 
thought  it  was  the  same  as  the  parabola.  Its  true  nature  was 
first  demonstrated  b}'  James  Bernoulli.  This  curve  has  also 
several  curious  properties. 

1.  If  the  chain  were  made  of  a  great  man}'  short  pieces  of 
wood  or  metal  hinged  together  b}'  rivets,  like  the  inside  chain 
of  a  watch,  and  we  could  turn  it  up  in  the  same  form  it  has 
when  it  hangs,  it  would  stand  up  without  ftiUing  in,  and  be  a 
catenary  upside  down.  This  is  the  only  curve  that  possesses 
this  property.  2.  If  we  wish  to  make  the  strongest  possible 
arch  for  a  Drid^c,  we  should  make  it  in  the  form  of  a  cate- 
nary. 

For  other  facts  in  the  elements  of  geometry,  see  First  Les- 
sons in  Geometry,  by  Dr.  Thomas  Hill,  a  valuable  little  book. 

II.  Geometry  as  a  Science. 

The  previous  course  in  the  elements  of  Geometry  is  de- 
signed as  an  introduction  to  the  stud}'  of  the  subject  as  a 
science.  By  means  of  it,  pupils  will  become  familiar  with  the 
leading  ideas  and  truths  of  geometry,  and  thus  be  prepared 
for  a  more  intelligent  study  of  the  science  when  of  a  suitable 
age.  Pui'ils  may  begin  the  stud}'  of  geometry'  as  a  science 
s-hen  abo.  *  thirteen  or  fourteen  3'ears  of  age. 

I.  The  Nature  of  the  Study. — The  study  of  Geometry  as 
a  science  includes  Definitions^  Axioms^  Fodulates,  Theorems, 
Demonstrations,  Problems,  Solutions,  and  Apjdications.  We 
shall  speak  of  the  nature  and  methods  of  teaching  each  of 
these,  and  also  of  the  method  of  hearing  a  recitation  in 
geometry. 

Definitions. — The  Definitions  of  geometry  are  statements 
of  the  ideas  of  the  science,  or  a  description  of  the  quantities 
upon  which  we  reason.    They  are  examples  of  what  are  known 


TEACUING   GEOMETRY.  423 

as  logical  definitions ;  tliat  is,  they  define  by  genua  and  di(fer- 
en^m,  or  specific  difference.  Tliiis,  in  the  definition,  "A  tri- 
angle is  a  polygon  of  three  sides,"  polygon  is  the  generic 
term,  and  three  sides  is  the  differentia  or  specific  difference. 
No  science  presents  so  many  fine  examples  of  logical  defini- 
tions as  geometry. 

These  definitions  shonld  be  expressed  in  the  deductive 
form;  that  is,  we  shonld  begin  with  the  term  to  be  defined, 
and  pass  to  genus  and  differentia.  The  definitions  should  be 
stated  positively,  not  negatively,  telling  what  a  thing  is,  and 
not  what  it  is  not.  Thus,  the  old  definition,  "A  straight  line 
is  one  that  does  not  change  its  direction,"  etc.,  is  not  so  satis- 
factory as  the  positive  one,  "  A  straight  line  is  one  that  lies 
in  the  same  direction,"  etc. 

How  Teach. — In  teaching  the  definitions,  the  first  requisite 
is  that  the  pupils  have  a  clear  notion  of  the  tiling  defined. 
They  should  be  required  to  give  an  illustration  of  each  defini- 
tion in  which  there  may  be  the  least  difficulty.  This  point  is 
important,  as  pupils  are  often  found  trying  to  reason  from  a 
definition  when  they  have  no  clear  idea  of  the  quantity  de- 
fined. It  is  especially  necessary  with  pupils  of  good  memory, 
who  are  apt  to  rest  satisfied  with  a  form  of  words  without 
taking  the  trouble  to  see  clearly  what  is  meant  by  them. 

Care  should  be  taken  to  see  that  the  definitions,  as  given  by 
the  pupil,  are  strictly  accurate.  The  language  of  the  author 
should  be  insisted  upon,  unless  the  teacher  or  pupil  can  im- 
prove the  definition,  which,  in  such  a  science  as  geometry, 
will  be  seldom  possible.  Most  of  the  definitions  are  classic 
with  culture  and  age,  and  have  become  fixed  in  form,  and  will 
not  admit  of  improvement.  It  is  an  excellent  exercise  to 
show,  by  question  and  illustration,  the  importance  of  the 
prominent  points  of  a  definition,  and  how  any  departure  from 
the  statement  will  vitiate  the  correctness  of  the  definition. 
A  proper  study  of  the  definitions  of  geometry  may  be  made 
a  source  of  excellent  mental  discipline. 


424  METHODS   OF   TEACHING. 

Axioms. — The  Axioms  of  geometry  are  the  self-evident 
truths  which  pertain  to  the  subject.  These  truths  lie  at  the 
basis  of  the  science;  they  are  the  foundation  upon  which  all 
the  other  truths  rest.  They  express  the  fundamental  and 
necessary  relations  of  quantity,  and  depend  for  their  existence 
on  no  truths  which  lie  behind  them.  These  truths  are  intu- 
itive; they  are  not  the  result  of  reasoning.  The  mind  is  so 
constituted  that  it  knows  them  to  be  true  upon  the  mere  an- 
nouncement or  contemplation  of  them,  and  neither  asks  nor 
needs  an}'  proof  of  them. 

Two  Kinds. — There  are  two  kinds  of  axioms  in  geometry; 
those  which  pertain  to  quantity  in  general,  and  those  which 
grow  out  of  the  particular  quantity  considered.  Examples 
of  the  former  class  are,  "  Things  that  are  equal  to  the  same 
thing  are  equal  to  one  another;"  "If  equal  quantities  be 
equall}'  increased  or  diminished,  the  results  will  be  equal." 
These  apply  to  arithmetic  and  algebra,  as  well  as  to  geometry. 
Examples  of  the  second  class  are,  "All  right  angles  are  equal 
to  one  another;"  "  The  radii  of  a  circle  are  all  equal."  These 
arise  out  of  the  particular  kind  of  quantity  considered,  and 
apply  only  to  geometry. 

Their  Use. — The  use  of  axioms  in  reasoning,  as  usually 
stated,  is  that  they  are  general  truths  which  contain  all  the 
particular  truths  of  the  science.  According  to  this  view,  the 
geometer  needs  onl}'  to  anah'ze  the  axioms,  and  he  will  find  in 
them  all  the  truths  of  the  science.  In  reasoning,  he  onl}-  un- 
folds these  general  truths  and  evolves  the  special  truths  which 
he  finds  contained  in  them.  This  view  of  the  subject  admits 
of  question.  It  maj-  be  pleasant  for  one  to  suppose  that 
when  he  knows  the  axioms  of  a  science,  he  has  in  his  mind, 
potentially  if  not  actually,  the  entire  science;  but  it  does  not 
seem  to  express  a  scientific  truth.  A  general  formula  ma}' 
truly  be  said  to  contain  many  special  truths  which  may  be 
derived  from  it;  but  no  axiom  in  this  sense  can  be  named  that 
contains  the  other  truths  of  geometry. 


TEACHING  GEOMETRY.  425 

Another  view  is  that  axioms  are  the  laws  which  guide  us  in 
reasoning:  they  are  the  laws  of  comparison  or  inference. 
Thus,  if  we  wish  to  compare  A  and  B,  seeing  no  relation 
directly  between  them,  we  may  compare  each  to  C ;  and  prov- 
ing that  they  are  both  equal  to  C,  we  infer  that  they  are  equal 
to  each  oiher.  The  law  that  governs  this  comparison,  and 
enables  us  to  make  the  inference,  is  the  axiom.  Things  that 
are  equal  to  the  same  thing  are  equal  to  one  another.  So  in 
comparing  parts  of  the  circle,  we  must  always  bear  in  mind 
the  truth  that  the  radius  is  half  of  the  diameter ;  but  it  can- 
not be  truly  said  that  this  axiom  contains  other  truths. 

It  is  also  true  that  an  axiom  may  be  one  of  the  premises  of  a 
syllogism  from  which  a  conclusion  is  drawn.  Thus  in  a  dem- 
onstration we  may  see  a  line  A  equal  to  a  radius  B  of  a  circle, 
but  radius  B  is  equal  to  radius  C  of  the  same  circle ;  there- 
fore, this  line  A  is  equal  to  radius  C.  In  this  case  the  axiom 
of  equal  radii  is  neither  a  general  truth  containing  other 
truths  nor  a  law  of  reasoning.  Axioms  may  thus  perform 
several  offices  in  a  demonstration ;  but  they  are  always  first 
truths,  beyond  which  we  cannot  go  in  thought. 

How  Teach. — In  teaching  the  axioms,  the  pupil  should  be 
required  to  give  an  exact  statement  in  the  language  of  the 
book,  unless  it  can  be  improved.  No  awkward  or  half-way 
statement  should  be  accepted  as  satisftictory.  He  should  also 
be  required  to  illustrate  the  axiom,  that  the  teacher  may  be 
sure  he  has  a  clear  conception  of  the  truth  he  is  stating. 

Postulates. — An  axiom  may  be  defined  as  a  self-eviden' 
theorem.  A  self-evident  problem  is  called  a  Postulate.  Tha« 
it  will  be  granted  that  "a  straight  line  may  be  drawn  froir 
one  point  to  another,"  or  that  "  two  lines  may  be  constructed 
equal  to  each  other."  The  postulates  bear  the  same  relation 
to  problems  that  axioms  do  to  theorems.  The  same  remarks 
will  apply  to  the  teaching  of  them  that  we  have  already  made 
with  respect  to  teaching  axioms. 

Reasoning. — All  reasoning  is  the  comparison  of  two  ideas 


4.26  METHODS   OF   TEACHING. 

through  their  relation  to  a  third.  Thus,  suppose  I  see  no  re- 
lation between  A  and  B,but  upon  looking  at  atiiird  quantity, 
C,  I  perceive  tliat  A  equals  C,  and  also  that  B  equals  C ;  and 
I  can  then  infer  that  A  equals  B,  I  thus  compare  A  and  B 
through  their  common  relation  to  the  tliinl  quantity,  C ;  C 
thus  stands  intermediate  between  A  and  B,  and  the  process  is 
called  a  process  of  mediate  or  indirect  comparison. 

This  is  the  general  nature  of  the  reasoning  of  geometi;. 
In  its  application  to  geometry  reasoning  assumes  two  diriii- 
ent  forms,  wluch  may  be  distinguished  as  the  analytic  and 
synthetic  methods.  The  analytic  method  is  adapted  to  the 
discovery  of  truth;  the  synthetic  method  is  used  in  proving 
a  truth  when  it  has  already'  been  discovered. 

Synthetic  Method— The  Synthetic  Method  of  proving  a 
truth  already  known  is  called  demonstration.  Demonstration 
begins  with  self-evident  truths  or  truths  already  proved  ;  and 
passes,  step  by  step,  to  the  truth  to  be  proved.  There  are 
two  distinct  methods  of  demonstration.  The  simplest  form 
Is  that  in  which  figures  are  directly  compared  by  applying  one 
to  another.  This  is  called  the  method  by  superposition.  It 
is  used  in  proving  the  equality  of  polygons  and  also  of  some 
of  the  volumes.  The  more  general  form  of  demonstration  is 
that  in  which  truths  are  proved  by  a  reference  to  the  defini- 
tions and  axioms,  or  to  some  principle  previously  proved. 

Analytic  Method.— The  Analytic  Method  begins  with  the 
thing  required,  and  traces  the  relation  between  the  various 
elements,  till  we  arrive  at  some  known  truth.  It  is  a  kind  of 
going  back  from  the  result  sought,  by  a  chain  of  relations,  to 
what  has  been  previously  established.  In  the  synthetic 
method,  we  pass  through  every  step,  from  the  simplest  self- 
evident  truth  to  the  highest  truth  of  the  science.  In  the 
process  of  analysis,  we  pass  over  the  same  path,  descending 
from  the  higher  truths  to  the  simpler  and  fundamental  truths. 

Analysis  is  the  method  of  discovery;  synthesis  is  the 
method  of  presentation.     The  one  has  for  its   object  to  find 


TEACHING   GEOMETRY.  427 

unkuown  truths;  the  other  to  prove  known  truths.  Fre- 
quently both  methods  are  employed  simultaneously,  when  the 
object  is  to  discover  new  theorems,  or  to  find  the  solution  of 
new  problems;  but  when  we  wish  to  prove  to  others  the  truths 
already-  known,  the  synthetical  method  is  usually  preferred. 

Reductio  ad  Abffui'duvi. — There  is  a  form  of  reasoning 
which  is  analytic  in  its  character,  known  as  the  reductio  ad 
absurdum.  It  consists  in  supposing  that  the  proposition  to 
be  proved  is  not  true,  and  then  showing  that  such  a  hypothi?- 
sis  leads  to  a  contradiction  of  some  known  truth.  This  proves 
a  theorem  to  be  true  by  simplv  showing  that  it  cannot  be 
false.  The  method  is  frequently  used  to  prove  the  converse 
of  a  proposition,  when  there  is  no  good  direct  method  ;  it  is 
also  used  in  treating  incommensurable  quantities. 

This  method  of  reasoning  is  also  called  a  demonstration , 
and  is  called  the  Indirect  Method^  to  distinguish  it  from  the 
other,  which  is  called  the  Direct  Method.  The  indirect 
method  is  not  considered  as  satisfactory^  as  the  direct  method, 
and  should  never  be  used  except  when  no  good  direct  method 
can  be  found. 

Errors  in  Reasoning. — There  are  two  errors  4n  reasoning 
into  which  3'oung  geometricians  are  liable  to  fall.  The  first  is 
called  Reasoning  in  a  Circle;  the  second  is  called  Begging  the 
Question.  We  reason  in  a  circle,  when,  in  demonstrating  a 
truth,  we  employ  a  second  truth  which  cannot  be  proved  with- 
out the  aid  of  the  truth  we  are  tr^aug  to  demonstrate.  We  are 
said  to  beg  the  question,  when,  in  order  to  establish  a  proposi- 
tion, we  emplo}'  the  proposition  itself. 

Practical  Problems. — A  radical  defect  of  most  of  our 
text-books  on  geometr}-  is  that  the}-  present  the  subject  so 
abstractly  that  when  the  pupil  has  completed  his  course,  he  is 
often  unable  to  make  any  practical  application  of  what  he  has 
learned.  This  defect  can  be  supplied  by  requiring  the  i)upils 
to  apply  the  principles  of  the  science  to  practical  examples. 
Such  applications  will  show  them  the  use  of  the  principles. 


^.2^  METHODS    OF   TEACHING. 

and  they  will  thus  understand  it  better  and  remember  u 
longer.  They  will  also  place  a  higher  value  on  the  science  on 
account  of  their  being  able  to  apply  their  knowledge  to  some 
practical  purpose.  These  applications  will  also  add  an  inter- 
est to  the  study  that  it  cannot  possess  by  the  purely  abstract 
method.  Every  text-book  in  geometry  should  be  supplied 
with  a  large  collection  o^  practical  examples. 

Undemonstrated  Theorems. — Another  defect  in  the  teach- 
ing of  geometry  has  been  the  lack  of  matter  for  original 
thought.  The  study  as  usually  pursued  does  not  give  train- 
ing to  the  inventive  powers  of  the  student.  He  is  required  to 
learn  the  demonstrations  of  the  text-book,  but  he  has  no 
undemonstrated  theorems  to  test  his  own  geometrical  powers 
and  to  train  him  to  reason  independently  of  the  text-book. 
To  remedy  this  defect,  he  should  be  given  a  collection  of 
theorems  for  original  thought,  and  be  required  to  try  his 
powers  of  reasoning  in  finding  out  the  demonstration  for 
himself. 

These  theorems  should  be  easy  at  first,  and  gradually  in- 
crease in  difficulty  as  the  pupil  gains  strength  for  the  work. 
They  may  lie  mingled  with  the  propositions  of  each  book 
(geometry  is  usually  divided  into  a  number  of  books),  or  they 
may  be  placed  at  the  close  of  each  book.  The  latter  method 
is  preferred  with  most  pupils,  as  they  should  be  quite  familiar 
with  the  propositions  of  any  given  book  before  they  are  pre- 
pared to  apply  these  principles  to  the  investigation  of  other 
truths.  One  original  theorem  each  day  to  apply  the  prin- 
ciples gone  over,  in  connection  with  two  or  three  theorems  of 
the  following  book,  will  make  a  very  interesting  exercise.  At 
the  close  of  the  text-book,  there  should  be  a  large  «umber  of 
miscellaneous  theorems  for  original  thought. 

This  is  the  method  used  in  arithmetic  and  algebra,  and  it 
seems  surprising  that  it  has  not  been  more  generally  em- 
ployed in  geometry.  Several  authors  seem  recently  to  have 
realized  the  importance  of  such  exercises,  and  have  occasion 


TEACHING   GEOMETRY.  429 

ally  given  some  practical  problems,  and,  in  one  or  two  in- 
stances, a  collection  of  undemonstrated  theorems.  In  the 
author's  work  on  geometr3^,  such  problems  and  theorems  are 
a  prominent  and  essential  part  of  the  plan. 

II.  The  Recitation. — The  several  things  to  consider  under 
the  recitation  in  geometry  are:  1.  The  assignment  of  the 
theorems ;  2.  The  construction  of  the  diagrams ;  3.  The  dem- 
onstration ;  4.  The  criticism;  5.  Xew  matter. 

Assignment. — The  theorems  may  be  assigned  to  the  pupils 
in  various  waj's.  They  ma}-  be  given  out  at  random,  without 
any  reference  to  the  ability  of  the  class;  or,  if  there  are  some 
in  the  class  who  are  not  very  strong  in  the  branch,  the  easier 
propositions  may  be  given  to  them.  The  best  way  probably' 
is  to  assign  by  chance,  which  may  be  done  by  writing  the 
numbers  of  the  propositions  on  small  pieces  of  paper,  and  re- 
quiring the  pupils  to  draw  these  papers.  It  is  suggested  that 
at  least  one  da3''s  review  lesson  should  be  included  in  each 
recitation,  the  class  taking  three  or  four  propositions  in  ad- 
vance, and  the  same  number  in  review. 

Construction, — The  pupil  haxing  received  a  theorem, 
should  be  required  to  go  to  the  board  and  construct  the  dia- 
gram without  any  reference  to  the  book.  The  lines  should  be 
drawn  by  free  hand,  and  not  with  the  aid  of  a  ruler.  The 
letters  of  the  diagram  should  be  placed  at  random,  and  dif- 
ferent from  the  order  in  the  book,  in  order  to  preA'ent  a  recita- 
tion from  memory.  Figures  in  place  of  letters  may  often  be 
used  in  marking  the  diagrams.  It  will  add  interest  also  for 
one  pupil  to  construct  the  diagram  for  another  pupil,  each 
thus  constructing  the  figures  of  one  proposition,  and  demon- 
strating another. 

Demonstration. — In  demonstrating  the  theorems,  the 
pupil  should  stand  at  the  board  in  an  erect  and  easy  attitude, 
his  face  turned  partly  toward  the  class,  and  the  pointer  being 
in  the  hand  next  to  the  board.  The  theorem  should  first  be 
stated  clearlj'  and  precisely,  and  in  the  language  of  the  book, 


430  METHODS    OF   TEACHING. 

unless  it  can  be  eriualed  or  improved.  The  deraonstration 
should  be  clearl}'  and  logically  presented,  the  definitions  and 
axioms  referred  to  by  number  or,  with  beuinners,  by  repeti- 
tion, and  previous  theorems  referred  to  by  number  of  book 
and  theorem.  When  the  demonstration  involves  several  pro- 
[jortions,  these  may  be  written  out  on  the  board  and  be 
pointed  at  in  the  demonstration. 

It  will' be  well  also  for  the  pupil  to  write  out  an  analysis  of 
the  course  of  reasoning  involved  in  a  demonstration.  Some- 
times an  analysis  merely  of  the  references  or  dependent  truths 
may  be  written.  Sometimes  the  pupil  may  be  required  to 
write  an  analysis  of  all  the  principles  involved  in  the  demon- 
stration, tracing  each  truth  all  the  way  back  to  the  definitions 
and  axioms.  Such  an  exercise  will  be  found  most  valuable  in 
giving  pupils  a  thorough  knowledge  of  the  subject. 

Criticism. — At  the  close  of  tlie  recitation  of  any  pupil, 
the  members  of  the  class  who  have  observed  any  errors  may 
be  called  upon  to  point  them  out.  These  may  consist  of  the 
omission  of  necessary  links  in  the  chain  of  reasoning,  the 
omission  or  misquoting  of  references,  etc.,  etc.  Pupils  who 
have  a  shorter  or  better,  or  even  a  different  method,  may  be 
called  upon  to  give  it.  Errors  unnoticed  by  the  pupils,  may 
then  be  pointed  out  b}'  the  teacher. 

Quesfioniuf/. — The  teacher  should  quiz  the  pupil  on  his 
demonstration.  He  should  ask  questions  like  the  following: 
What  kind  of  demonstration  is  it?  Why  do  you  begin  as  you 
do?  Why  do  you  prove  such  a  thing  equal  to  such  a  thing? 
What  relation  does  this  proposition  bear  to  the  preceding 
proposition  ?  What  application  can  you  make  of  this  truth  ? 
Show  its  application,  etc. 

Outlines. — At  the  close  of  a  book,  the  pupil  should  be  re- 
quired to  give  an  outline  of  the  book;  show  the  design  of 
it;  show  what  propositions  reach  final  truths,  and  what  prop- 
ositions were  merely  auxiliary:  show  the  relation  of  each 
proposition  to  the  chain  of  logic,  and  how  the  chain  would 


TEACHING   GEOMETRY.  -iSl 

be  broken  by  the  omission  of  any  proposition ;  etc.  By  fol- 
lowing these  suggestions,  the  teacher  will  make  geometry  a 
delightful  study  to  his  pupils,  and  a  most  valuable  means  of 
mental  culture. 

New  Matter. — If  the  teacher  has  any  new  matter,  it  may 
he  presented  at  this  time.  He  may  give  a  discussion  of  the 
general  nature  of  the  lesson,  show  the  excellence  or  defect  of 
the  method  of  development  made  use  of,  and  make  a  compar- 
ison between  the  method  of  treatment  used  In*  the  author  and 
that  of  other  authors.  He  should  then  assign  the  nest  les- 
son, and  present  any  suggestions  concerning  it  that  may 
seem  advisable. 

Conclusion. — In  conclusion,  we  would  urge  teachers  to 
introduce  the  elements  of  geometry  into  our  public  schools. 
A  little  less  arithmetic,  if  need  be,  in  order  to  present  some 
geometry,  would  be  an  advantage.  We  trust  that  teachers  may 
realize  the  importance  of  the  subject,  and  endeavor  to  awaken 
a  deeper  interest  in  the  beautiful  science  of  form — a  science 
over  which  the  ancient  sages  mused  with  such  deep  enthu- 
siasm, and  to  which  the  achievements  of  modem  art  and 
invention  are  so  largely  indebted. 


CHAPTER  VII. 


TEACHING    ALGEBRA. 


ALGEBRA  is  that  branch  of  mathematics  which  inves- 
tigates quantity  by  means  of  general  characters  called 
symbols.  The  term  originated  with  the  Arabs,  and  comes 
from  al-gabr,a  reduction  of  parts  to  a  whole.  The  definition 
given  states  the  general  character  of  the  subject,  though  it  is 
diflicult  to  give  a  definition  that  fixes  precisely  its  province 
and  object. 

Relation  to  Arithmetic. — Algebra  in  its  elements  is  closely 
related  to  arithmetic.  It  had  its  origin  in  arithmetic,  and  its 
fundamental  ideas  and  operations  are  arithmetical.  Its  sym- 
bols of  quantity  were  at  first  merely  general  symbols  of  num- 
bers, and  its  fundamental  operations  of  addition,  subtraction, 
etc..  were  entirely  similar  to  those  of  arithmetic.  On  account 
of  this  relation,  algebra  has  been  called  a  kind  of  general  arith- 
metic. Newton  called  it  Universal  Arithmetic.  D'Alembert 
regards  it  as  a  special  branch  of  tl^e  general  science  of  num- 
bers ;  and  divides  arithmetic  into  Numerique,  special  arith- 
metic, and  Algebre,  general  arithmetic. 

Wider  View. — This  view  of  the  nature  of  algebra  is  now 
too  narrow.  Algebra  has  ti-anscended  the  bounds  of  its  ori- 
gin. It  reaches  from  arithmetic  over  into  geometry,  including 
continuous  as  well  as  discrete  quantity.  From  the  generality 
of  its  symbols,  also,  man}^  ideas  and  processes  arise  which  have 
no  meaning  or  use  in  arithmetic ;  as  negative  and  imaginary 
quantities,  the  solution  of  higher  equations,  etc. 

Another  important  difference  is,  that  iu  arithmetic  the  com 
putations  being  made  as  they  arise,  all  traces  of  the  interme- 
diate steps  are  lost,  and  the  result  is  applicable  to  a  single 
case  only ;  wliereas  in  algebra  the  result  is  general,  and  con- 

(482  > 


TEACHING   ALGEBRA.  433 

tains  implicitly  the  answer  to  all  problems  of  the  same  general 
class.  The  combination  of  alo-ebraic  symbols  leads  to  expres- 
sions called  formidas,  in  whicli  the  operations  are  indicated 
rather  than  performed,  and  which  admit  of  interpretation. 
These  formulas  often  express  a  general  truth  corresponding 
to  a  theorem,  which  arithmetic  can  verify  in  particular  cases  ; 
as  (a-{-b)(a — b)  =  a'^ — 6^,  and  x= — p±'^q-\-p^. 

Conife's  View, — Comte  divides  mathematics  into  geomefri/ 
and  analysis  or  calculus.  Calculus  embraces  algebraic  calcu- 
lus, or  algebra,  and  arithmetical  calculus,  or  arithmetic.  Al- 
gebra is  defined  "  as  having  for  its  object  the  resolution  of 
equations,''^  which  signifies  "  the  transformation  of  implicit 
functions  into  equivalent  explicit  ones."  Arithmetic  is  defined 
as  the  science  which  "  ascertains  the  values  of  functions.''^ 
"Algebra  is  the  calculus  of  functions ;''''  and  "Arithmetic  is 
the  calculus  of  values."  Sir  William  Rowan  Hamilton,  the 
author  of  Quaternions,  defines  algebra  as  the  science  of  time, 
which  De  Morgan  changes  to  the  calculus  of  succession. 

Symbols. — The  symbols  of  algebra  are  of  three  general 
classes  ;  Symbols  of  Quantity,  Symbols  of  Relation,  and  Sym- 
bols of  Operation.  The  Symbols  of  Quantity  are  of  two 
kinds;  symbols  of  knoivn  quantities  and  symbols  of  unknown 
quantities.  They  include  also  the  two  limits  of  quantity, 
zero,  0,  and  infinity,  oo.  The  Symbols?  of  Operation  include 
the  signs  of  all  the  o[)erati()ns  to  which  quantity  can  be  sub- 
jected. The  Symbols  of  Relation  include  the  s^^mbols  which 
arise  in  comparing  quantity;  as,  =,:,::,>■•<,  etc. 

The  symbols  of  quantity  apply  to  continuous  as  well  as  dis- 
crete quantity.  Thus  a  and  b  may  represent  two  lines  as  well 
as  two  numbers.  If  these  lines  have  a  common  unit,  then  a 
and  b  may  be  regarded  as  representing  the  lines  numerically ; 
but  when  the  lines  have  no  common  unit,  a  and  6  denote  them 
as  continuous,  and  not  as  discrete  quantity. 

Generalization. — The  spirit  of  generalization  in  algebra  is 
the  source  of  many  of  its  ideas  and  processes.  From  this  we 
19 


434  METHODS   OF   TEACHINa. 

have  the  negative  quantity,  the  fractional  and  negative  expo- 
nent, the  imaginary  quantity,  etc.,  each  of  which  admits  of 
explanation  and  leads  to  new  conceptions  in  the  science 
Thus,  the  sign  of  subtraction  is  primarily  used  to  denote  that 
a  Quantity  is  to  be  subtracted  ;  but  if  we  subtract  a  from  the 
quantity  a — b,  we  have  a  remainder  of  — b,  the  interpretation 
of  Avhich  gives  us  the  idea  of  a  Negative  Quantity. 

The  Fractional  Exponent  originates  in  the  same  way.  Hav- 
ing agreed  to  indicate  a  power  b}'  an  exponent,  b}'  generaliza- 
tion we  have  a";  and  since  n  can  represent  anv  quantit}-,  it 

may  represent  a  fraction,  as  |,  and  we  have  a*.  This  expres- 
sion being  interpreted,  we  find  means  the  third  power  of  the 
fourth  root  of  a.  Or,  having  the  rule  that  the  root  of  a  quan- 
tity may  be  obtained  by  dividing  its  exponent,  in  extracting 

3 

the  4th  root  of  a^  we  reach  the  same  result,  a^. 

The  Negative  Exponent  has  a  similar  origin.  Since  the 
general  exponent  may  represent  any  quantity,  it  may  repre- 
sent a  negative  quantity,  and  we  may  thus  have  a"** ;  a  new 
idea  which  needs  interpretation.  Or,  if  we  divide  a"  by  a-** 
according  to  the  general  rules  of  division,  we  also  reach  the 
expression  a-^ ;  and  this  we  find  denotes  the  reciprocal  of  a" , 

1 

or  that  a—^=  — 
a« 

The  Imaginary  Quantity  arises  b}'  a  similar  process  of  gen- 
eralization. In  the  general  expression  v^a,  n  ma}'  be  even 
and  a  may  he  negative,  which  gives  us  such  exjjressions  as 
v^-4,v  -8,  v^_l6,  etc.  Or,  given  general  methods  of  solving 
quadratic  equations,  imaginary  expressions  ma}-  arise  from 
the  solution  of  such  equations,  as  x'^=:  —  4,  or  x"^  —  2j:= — 5. 
This  expression  must  also  be  interpreted.  'In  the  same  way, 
other  ideas  arise  in  algebra  from  the  generality  of  the  notation 
and  of  the  methods  used 

I>ivisioH  of  Subject. — The  science  of  algebra  admits  of 
the  same  fundamental  divisions  as  arithmetic.  These  pro- 
cesses are  all  included  under  the  three  heads ;  Synthesis,  Analy- 


TEACHING   ALGEBRA.  435 

sis,  and  Comparison.  The  fnndamenta!  operations  are  Addi- 
tion, Subtraction,  Multiplication,  and  Division.  The  deriva- 
tive or  secondary  processes  are  Composition,  Factoring, 
Common  Multiple,  Common  Divisor,  Involution,  and  Evo- 
lution. Comparison  gives  rise  to  the  Equation,  Ratio, 
Proportion,  the  Progressions,  etc. 

Each  of  these  processes,  on  account  of  the  generality  of  the 
symbols  and  operations,  gives  rise  to  processes  and  expres- 
sions not  found  in  arithmetic.  In  respect  to  the  new  process 
called  Composition,  we  remark  that  its  scientific  necessity  is 
seen  from  the  fact  that  each  analytic  process  has  its  corre- 
sponding synthetic  process.  Thus  addition  is  synthetic, 
subtraction  is  analytic,  multiplication  is  synthetic,  division  is 
analytic,  etc.;  it  follows, therefore,  that  there  should  be  a  syn- 
thetic process  corresponding  to  the  analytic  process  of  Fac- 
toring. This  process  we  have  called  Composition;  and  its 
value  is  especially  apparent  in  algebra,  on  account  of  the 
seveval  interesting  and  practical  cases  which  it  embraces. 

The  Equation. — The  fundamental  process  of  comparison 
in  algebra  is  that  of  the  Equation.  The  equation  makes  its 
api>earance  in  arithmetic,  but  is  not  of  sufficient  distinctive 
impoi'tance  to  be  regarded  as  a  distinct  part  of  the  science. 
In  algebra,  however,  it  is  of  fundamental  importance  ;  and 
gives  the  science  its  principal  value.  Indeed,  so  largely  does 
it  enter  into  the  subject,  that  it  would  not  be  very  far  from 
the  truth  to  say  that  algebra  is  the  science  of  the  equation. 

The  principal  use  of  the  equation  is  to  compare  unknown 
quantities,  variously  involved,  with  known  quantities,  the 
object  being  to  find  the  value  of  these  unknown  quantities. 
In  the  effort  to  disengage  the  unknown  quantity  from  the 
known  and  find  an  expression  for  its  value  in  known  terms, 
we  discover  methods  of  procedure  called  the  solution  or  reso- 
lution of  the  equation.  The  solution  of  the  equation  gives 
rise  to  several  processes,  among  which  are  Transposition, 
Substitution,  Completing  the  Square,  etc. 


4,Z^  METHODS   OF  TEACHINQ. 

The  solution  of  the  general  equation  has  never  been  deter- 
mined, and  is  no  doubt  impossible.  The  solution  of  the  cubic 
and  bi-quadratic  is  attended  with  difficulties  that  render  the 
present  methods  not  entirely  satisfactor3'^ ;  and  the  solution  of 
the  general  equation  beyond  the  fourth  degree  has  never  been 
accomplished  and  is  believed  to  be  impossible.  But  though 
no  solution  of  the  general  equation  has  been  found,  many  pro- 
perties have  l>een  discovered  that  enable  us  to  know  much 
about  their  roots.  These  properties  embrace  some  of  tlie 
most  beautiful  things  in  the  science  of  mathematics,  such  as 
Descartes'  Rule,  Sturm's  Theorem,  etc.,  and  confer  immor- 
tality upon  their  discoverers.  Besides  these,  we  have  in 
Horner's  Method  a  general  method  of  solving  all  numerical 
equations  that  have  real  roots. 

Reasoning. — The  reasoning  of  algebra  is  essentially  de- 
ductive. The  comparison  of  quantities  is  usually  that  of 
equals,  the  relation  being  expressed  by  the  equation.  This 
equation  is  operated  upon  in  various  ways,  all  the  operations 
being  controlled  by  the  axioms  of  the  science.  All  the  ope- 
rations of  addition,  subtraction,  transposition,  substitution, 
etc.,  are  governed  by  axiomatic  principles,  and  this  makes  the 
reasoning  deductive.  . 

Induction. — Though  algebra  is  a  deductive  science,  it  is 
possible  to  derive  some  of  its  truths  by  induction.  Indeed, 
man}'  of  the  first  generalizations  of  its  symbols  are  inductive 
in  their  character.  Several  of  its  leading  truths  were  discov- 
ered by  an  inference  from  particular  cases,  and  were  after- 
ward demonstrated.  Newton's  Binomial  Theorem  was  derived 
in  this  way  ;  and  it  is  presented  in  this  manner  to  the  students 
of  elementary  algebra.  The  divisibility  of  a"  —  6"  by  a—b 
ma}-  be  inferred  from  the  truth  of  the  several  cases  a^ — b"^, 
a^—b^,  a* — &*,  etc. 

Mathematical  Induction. — There  is  a  method  of  reason- 
ing in  algebra  called  mathematical  induction.,  which  differs 
from  pure  induction.     Mathematical  induction  derives  a  gen- 


TEACHING   ALGEBRA.  437 

eral  truth  by  showing  that  what  is  true  in  n  cases  is  true  in 
At+l  cases  ;  while  pure  induction  proceeds  upon  the  principle 
that  what  is  true  in  many  cases  is  true  in  all.  The  principle  of 
mathematical  induction  is  used  by  many  writers  in  proving 
that  o"  —b^  is  divisible  by  a— 6,  and  also  in  giving  a  general 
demonstration  to  the  Binomial  Theorem. 

History  of  Algebra. — The  first  known  treatise  on  algebra 
is  found  in  the  Arithmetic  of  Diophantus,  written  in  the 
fourth  century.  Though  not  presenting  a  complete  treatise 
on  algebra,  it  lays  an  excellent  foundation  for  the  science.  It 
contains  the  first  enunciation  of  the  rule  that  "  minus  multi- 
plied by  minus  produces  plus ;"  solves  such  problems  as 
"  Find  two  numbers  such  that  the  sum  or  difference  of  their 
squares  are  squares;"  and  then  proceeds  to  the  solution  of  a 
peculiar  class  of  problems  which  belong  to  what  is  now  called 
indeterminate  analysis. 

It  is  supposed  that  some  of  the  principles  were  known  be- 
fore the  time  of  Diophantus  ;  but  he  greatly  enriched  the 
science  with  new  applications.  He  shows  great  skill  in  the 
subject,  presenting  some  elegant  solutions,  and  is  regarded  as 
the  author  of  Diophantine  Analysis.  The  celebrated  Hypatia 
composed  a  commentar}'^  on  Diophantus,  which  is  now  lost. 
The  work  of  Diophantus  was  discovered  at  Rome,  in  the 
Vatican  library,  about  the  middle  of  the  sixteenth  century, 
having  probal)ly  been  brought  there  from  Greece  when  the 
Turks  captured  Constantinople. 

Algebra  was  introduced  into  Europe  by  the  Arabs,  who 
had  carefully  collected  the  writings  of  the  Eastern  mathemati- 
cians and  written  commentaries  upon  them,  A  copy  of  an 
Arabic  original  is  preserved  in  the  Bodleian  Library  at  Oxford, 
bearing  a  date  of  transcript  corresponding  to  the  3'ear  1342. 
This  work  is  supposed  to  have  been  derived  from  the  Hin- 
doos. Very  few  additions  to  the  science  seem  to  have  been 
made  by  the  Arabs,  though  they  cultivated  it  with  great 
enthusiasm.     The  science  of  algebra  was  introduced  into  Italy 


438 


METHODS   OF   TEACHING. 


by  Leonardo,  a  merchant  of  Pisa,  who  had  travelled  exten- 
sivel}'  in  the  East,  in  a  work  composed  two  centuries  before 
the  invention  of  printing.  He  could  solve  equations  oi"  the 
first  and  second  degrees,  and  was  particularh'  skillful  in  tlie 
diophantine  analj^sis.  Like  the  Arabian  writers,  his  reason- 
ing was  expressed  in  words  at  length,  the  use  of  symbols 
being  a  much  later  invention. 

The  earliest  printed  book  on  algebra  was  corajjosed  by 
Lucas  di  Borgo,  a  Minorite  friar.  It  was  called  Summa  de 
Arithmetical  Geometria,  Proportioni,  et  Proportionalita^  and 
was  published  in  1494  and  again  in  1523.  It  followed  Leon- 
ardo very  closel}' ;  but  the  mode  of  expression  was  very  im- 
perfect, the  symbols  employed  being  a  few  abbreviations  of 
the  words  or  names  which  occurred  in  the  process  of  calcula- 
tion,— a  kind  of  short-hand  arithmetic.  The  application  was 
also  limited,  being  confined  to  the  solution  of  certain  problems 
about  numbers.  It  included  the  solution  of  equations  of  the 
first  and  second  degrees,  the  latter  being  divided  into  cases, 
each  of  which  was  solved  by  its  own  particular  rule,  many 
of  which  were  derived  from  geometrical  constructions,  and 
expressed  in  Latin  verses  to  be  committed  to  memory. 

Up  to  the  fifteenth  century,  the  science  was  limited  to  the 
solution  of  equations  of  the  first  and  second  degrees.  In  1505 
Scipio  Ferreus,  a  professor  of  mathematics  in  Bononia,  dis- 
covered the  solution  of  a  particular  case  of  an  equation  of 
the  third  degree.  Ferreus  communicated  his  discovery  to  a 
favorite  scholar,  Florido,  who  challenged  Tartaglia,  a  noted 
mathematician,  to  a  trial  of  skill  in  solving  questions.  Tar- 
taglia had,  however,  discovered  the  solution  of  four  cases  of 
cubics,  and  came  off  victorious.  Cardan,  Professor  of  Mathe- 
matics at  Milan,  made  great  efforts  to  obtain  the  rules  of 
Tartaglia,  who  finallj'  consented  to  show  his  method,  which 
Cardan,  in  violation  of  an  oath  of  secrecy'  exacted  by  Tartag 
lia,  published  with  some  improvements,  in  a  work  he  was 
then  preparing.    Lewis  Ferrari,  a  pupil  of  Cardan,  soon  after- 


TEACHING   ALGEBRA.  439 

wards  discovered  the  solution  of  an  equation  of  the  fourth 
degree.     In   1572,  Bombelli,  an   Italian  mathematician,  pub- 
lished a  work  in  which  he  explained  the  natnre  of  the  irre- 
ducible  case  of  cubic  equations,  which  had  perplexed  Cardan. 
In  1540  Recorde  published  his  famous  Whetstone  of  WUte, 
in  which  the  sign  of  equality  first  appeared.     Vieta  (1540- 
1G03)  was  the  first  to  employ  general  characters  to  represent 
known  quantities,  which  was  a  great  step  in  advance.     He 
also  improved  the  theory  of   equations  and   gave   the    first 
method  of  solving  them   by   approximation.     Albert   Girard 
(1629),  a  Flemish   mathematician,  was  the   first  to   speak  of 
Imaginary  Quantities;  and   inferred  also  by  induction  that 
any  equation  has  as  many  roots  as  there  are  units  in  the  num- 
ber of  its  degree.     Thomas  Harriot  made  the  important  dis- 
covery that  every  equation  may  be  regarded  as  formed  by  the 
product  of  as  many  simple  equations  as  there  are  units  in  the 
number  expressing  its  order.     He  also  made  several  changes 
in  the  notation,  and  added   several  signs,  so   that  as  it  came 
from  his  hands  it  differed  very  little  from  its  form  at  the  pres- 
ent time.    Descartes  (1637)  made  one  of  the  greatest  improve- 
ments by  the  application  of  algebra  to  curved   lines,  which 
resulted  in  a  new  branch.  Analytical  Geometry. 

The  science  was  subsequently  enriched  by  Newton,  who  dis- 
covered the  binomial  theorem,  and  by  Euler,  who  made  exten- 
sive applications  of  it.  Lagrange  was  the  first  to  prove  that 
every  numerical  equation  has  a  root,  which  had  previously 
been  only  assumed.  Gauss,  1801,  developed  the  subject  of 
binomial  equations;  W.  G.  Horner,  in  1819,  published  his 
celebrated  method  of  solving  numerical  equations  ;  and  in 
1829  Sturm  made  known  his  beautiful  theorem  for  assigning 
the  position  of  the  real  roots  of  an  equation. 

The  latest  improvement  is  the  development  of  the  subject 
of  Determinants.  The  germ  of  this  theory  is  found  in  the 
writings  of  Leibnitz.  It  was  revived  more  than  fifty  years 
afterwards  by  Cramer,  and  was  extended  by  Gauss  and  others. 


440  METUODS   OF   TEACHING. 

It  has  received  its  latest  and  fullest  development  at  the  hands 
of  two  great  English  mathematicians,  Cayley  and  Sylvester. 

Method  of  Teaching  Algebra. 

We  shall  now  give  a  brief  discussion  of  the  method  of  teach- 
ing algebra.  We  shall  present  several  principles  to  guide  the 
teacher  in  the  instruction,  then  show  how  to  teach  some  of  the 
elementary  portions  of  the  subject,  and  then  close  the  article 
with  a  few  general  suggestions  to  the  teacher. 

Principles  of  Instruction. — There  are  several  general  prin- 
ciples which  should  guide  the  teacher  in  presenting  the  sub- 
ject of  algebra  to  the  beginner. 

1.  We  should  lead  the  jitipil  to  make  the  transition  from 
arithmetic  to  algebra;  algebra  grew  out  of  arithmetic.  This 
is  in  accordance  with  the  genesis  of  the  science.  It  is  also 
indicated  by  the  law  of  thought  from  the  particular  to  the 
general,  algebra  being  a  kind  of  general  arithmetic.  We 
should  introduce  algebraic  methods  while  teaching  arith- 
metic. Mental  arithmetic,  especially,  may  be  made  to  flow 
naturally  into  mental  algebra.  Algebraic  methods  may  also 
be  introduced  into  written  arithmetic,  as  in  percentage, /)= 
br ;  also  in  interest,  as  i=ptr ;  and  also  in  the  progressions, 
etc.  In  advanced  arithmetic,  many  of  the  subjects  should  be 
generalized  and  presented  in  algebraic  notation. 

2.  We  should  begin  algebra  with  concrete  problems,  and  not 
with  the  abstract  operations  of  the  science.  This  is  also  in 
accordance  with  the  laws  of  thought.  It  is  also  the  historic 
order;  algebra  was  an  outgrowth  of  the  attempt  to  solve  con- 
crete problems.  It  makes  the  subject  much  easier  for  pupils, 
as  they  catch  the  spirit  of  the  algebraic  method,  and  are  thus 
better  prejjared  to  understand  the  abstract  operations  of  the 
science.  The  more  recent  writers  on  elementary  algebra 
make  a  great  mistake  in  omitting  such  exercises  as  an  intro- 
duction to  the  subject. 

3.  The  pupil  should  have  a  thorough  drill  in  the  practice 


r 


TEACHINQ    ALGEBRA.  44] 

of  algebra.  Algebra  is  a  calculus,  and  the  pupil  needs  to  be- 
come skillful  in  algebraic  manipulations.  It  la  discouraging 
to  nave  pupils  in  analytical  geometr}-  and  calculus,  who  are 
constantly  making  mistakes  in  the  algebraic  operations. 
There  should  be  a  large  collection  of  examples  in  the  funda- 
mental rules,  fractions,  equations,  radicals,  etc.,  to  attbrd  the 
means  of  acquiring  this  skill.  The  teacher  of  elementary 
algebra  should  select  and  prepare  two  or  three  times  the  num- 
ber of  examples  found  in  any  ordinary  text-book  on  algebra, 
and  drill  his  pupils  on  them. 

Course  of  Instruction. — The  course  of  instruction  in  ele- 
mentary algebra  should  include  the  following  things:  1.  An 
Introduction,  including  the  solution  of  concrete  problems  and 
the  introduction  of  the  algebraic  symbols ;  2.  Algebraic  No- 
tation ;  3.  Explanation  of  the  Negative  Quantity  ;  4.  Funda- 
mental Operations;  5.  Secondary  Operations;  6.  Fractions; 
7.  Simple  Equations  ;  8.  Solution  of  Problems,  etc. 

1.  Introduction. — To  introduce  the  subject  of  algebra, 
take  a  simple  problem  in  mental  arithmetic,  and  write  out 
the  analysis  upon  the  board,  and  then  transform  this  analy- 
sis into  the  abbreviated  method  of  algebra.  To  illustrate,  take 
the  problem,  "  William  has  3  times  as  many  apples  as  Henry, 
and  both  have  24;  how  many  has  each?" 
Illustration.— By  arithmetic  we  solve  the  problem  as  follows : 

Henry's  number,  plus  three  times  Henry's  number,  equals  24; 

Hence  4  times  Henry's  number  equals  24  ; 

And  once  Henry's  number  equals  \  of  24,  or  6,  etc. 

Now,   if  we  represent  the  expression,  "  Henry's  number,"  by  some 

character,  as  the  letter  x,  the  solution  will 

be  made  shorter,  as  seen  in  the  margin.    If        f  P'^^  ^  times  z  equals  24, 
„  ^  i.,,.,.-  >>      J        hence  4  times  X  equals  24; 

we  now  use  3x  to  represent    3  tunes  x,    and        ^^^  ^^^^  ^  ^^^^{^  g^ 

4x  to  represent  "4  times  .r, "  the  symbol  = 

for  the  word  "equals,"  and  the  symbol  -\-  x+3x=24; 

for  the  word  "plus,"  the  solution  will  be  ^^^ 

still  shorter,  as  seen  in  the  margin.     This 

solution  is  purely  algebraic,  and  is  a  type 

of  the  entire  method  of  algebraic  reasoning. 

19* 


442  METHODS    OF   TEACUING. 

The  pupil  will  see  that  the  last  solution  is  the  same  as  the 
first,  except  that  we  use  characters  instead  of  words.  These 
characters  are  called  symbols.  The  pupil  may  then  be  shown 
that  2x,  Sx,  etc.,  means  "  2  times  x,"  "  3  times  a;,"  etc.;  that 
"  one-half  of  a:,"  "  2  thirds  of  .r,"  are  expressed  thus  :  ^x,  fx, 

X     2x 
or—,    — ,  etc.     He  may  also  be  told  that  an  expression  like 
2       3 

x+3j:=24,  is  called  an  equation.  The  pupil  should  then  bre 
drilled  on  the  solution  of  concrete  problems  until  he  is  familiar 
with  the  algebraic  idea,  and  the  fundamental  principles  of 
notation.  Problems  may  be  selected  in  which  all  the  simple 
elements  of  notation  may  be  gradually  introduced.  Symbols 
for  known  quantities  may  also  be  used.  For  classes  of  prob- 
lems, see  author's  Elementary  Algebra. 

2.  Algebrnic  Xotatioii. — The  pupil  is  now  ready  for  a  for- 
mal explanation  of  algebraic  notation.  The  various  symbols 
should  be  presented,  and  the  pupil  quite  thoroughly  drilled  in 
reading  and  writing  algebraic  expressions.  It  will  be  well 
also  to  drill  the  pupil  \i\  finding  the  numerical  value  of  alge- 
braic expressions  b}'  substituting  numbers  for  letters. 

3.  Negative  Quantity. — The  next  step  is  to  explain  the 
meaning  and  use  of  the  negative  quantity^  as  this  will  be 
needed  in  understanding  the  fundamental  operations.  We 
first  show  that  a  positive  quantity  means  an  additive  quantity, 
and  denotes  that  something  is  to  be  increased  by  it ;  and  that 
a  negative  quantity  is  a  subtractive  quantity,  and  denotes  that 
something  is  to  be  diminished  by  it.  We  next  lead  the  pupil 
to  see  that,  since  positive  and  negative  are  opposite  in  meaning^ 
the}'  may  be  used  to  represent  quantity  considered  in  opjjosite 
directions  or  senses.  Thus,  if  we  use  -f-  to  represent  a  per- 
son's gains  in  business,  we  may  use  —  to  represent  his  losses  : 
north  latitude  va.ay  be  denoted  b}'  -f-  and  south  latitude  by  — ; 
future  time  by  +  and  past  time  by  — ,  etc.  It  will  thus  be 
seen  that  the  symbols  -|-  and  —  may  indicate  the  nature  of 
quantity,  as  well  as  tiie  operations  to  be  performed  on  it. 


1 


TEACHIXQ   ALGEBRA.  443 

Principles. — We  next  establish  some  pi'inciples  pertaining 
to  the  negative  quantity.  Thus,  since  $8  united  with  $5  gain 
and  $5  loss  leaves  $8,  we  infer  that  uniting  -{-5  and  — 5  makes 
nothing,  or  that  uniting  a  poi<itive  and  negative  qxanfify  of 
the  same  absolute  value  amounts  to  nothing.  We  next  show 
that  in  algebra  a  po.-<itive  quantity  is  regarded  as  greater  than 
a  negative  quantity,  whatever  their  absolute  value.  Thus,  if 
we  unite  8  with  +4,  and  also  with  — 6,  the  first  result  is  12. 
and  the  second  2,  from  which  we  infer  that  +4  is  greater  than 
—  G.  Such  a  drill  on  the  nature  of  positive  and  negative 
quantities  is  absolutely  necessary  in  order  to  understand  their 
use  in  algebraic  addition  and  subtraction. 

4.  Addition. — Addition  is  most  convenient!}' treated  under 
two  cases:  1.  To  add  similar  quantities  ;  2.  To  add  dissimilar 
quantities.  The  first  case  embraces  two  sub-cases:  1.  'W'hen 
the  signs  are  alike;  2.  When  the  signs  are  unlike.  When  the 
terms  have  the  same  sign,  the  process  is  entirely  simple  ;  when 
they  have  unlike  signs,  the  process  needs  explanation. 

]\[ethods. — There  are  two  methods  of  explaining  this  case, 
Avhich  we  distinguish  as  the  Old  Method  and  the  New  Method. 
The  New  Method  introduces  the  idea  of  an  auxiliary  quantity; 
that  is,  it  assumes  that  a  positive  term  denotes  that  some 
quantity  is  increased  by  the  term,  and  a  negative  term 
denotes  that  some  quantity  is  diminished  by  the  term. 

Illustration — Pkob.  What  is  the  sum  of  T'l  and  A.a,  or — la  and — 4*<? 
Sol.  The  sum  of  7.?  and  4^  is  evidently  11-^  ;  and  the  sum  of  — "m  and  — \ii 
is  evidpntl}"-  — 11^.  Prob.  What  is  the  sum  of  7«  and  — \<t'^  Soi..  Plus 
la  denotes  Kmne,  qnnntity  incrensed  by  la,  and  — 4/;  denotes  some  quantity 
diminushed  hy  4'/.  ;  and  ani/  quantity  increased  by  la,  and  diminished  by 
ia,  is  evidently  increased  by  3'/  ;  hence  the  sum  of  7'/  and  — 4'/  is  f-oa. 
Prob  What  is  the  sum  of — 7'/  and  -\--ia  ?  SuL.  A  quantity  diminished 
by  ~a  and  increased  by  Aa  is  evidently  diminished  by  3'/  ;  hence  ihe  sum 
of  — la  and  -r4a  is  — 3.r.  We  may  also  explain  the  sum  of  la  and  — 4a 
as  follows:  la:=^i-\-^a;  and — 4a  united  with +4.x  is  zero.  Hence 
in  united  with  3a+4a  equals  +3a. 

5.  iS«ft<i'«ct/on.-- Subtraction    is    convenientl}'^    presented 


444  METHODS   OF   TEACHING. 

under  two  general  cases:  1.  When  the  terms  are  similar;  'z. 
When  the  terms  are  dissimilar.  The  former  includes  two  sub- 
cases :  1.  When  the  terms  have  like  signs  ;  2.  When  the  terms 
have  unlike  signs.  The  second  principal  case  includes  two 
sub-cases:  1.  Monomials;  2.  Polynomials. 

Methods. — There  are  several  methods  of  explaining  sub- 
traction, among  which  we  raa^'  mention  the  following :  1.  A 
new  method  ;  2.  Leibnitz's  method;  3.  Adding  to  both  terms; 
4.  Negative  quantity  less  than  zero;  6.  Latitude  and  longi- 
tude method.  The  new  method  makes  use  of  the  auxiliary 
quantity,  regarding  -j-2a  as  denoting  some  quantity  increased 
by  2a,  and  — 3a  as  denoting  some  quantity  diminished  by 
3a;  the  ''''some  quantity''''  being  used  as  auxiliary  in  the 
process. 

Illustration.  Neic  Method. — Pkob.  Subtract  la  from  4a.  Sol.  A 
quantity  increased  by  4a  is  evidently  'da  less  than  the  quantity  increased 
by  la  ;  hence  An  minus  la  equals  — 3a.  In  a  similar  manner  we  may 
explain  the  following  problems:  (2).  — la  minus  — 4a  ;  (3).  —4a  minus 
— 7a  ;  (4).  — la  minus  4a;  ioi  la  minus  — 4a;  (6l.  4a  minus  — 7a; 
(7).  — 4a  minus  7a.  Pros  Subtract  — c  from  a.  8ol,.  The  difference 
between  a  quantity  increased  by  a  and  diminished  by  c  is  evidently  tlie 
sum  of  a  and  c,  or  a+c  ;  hence  — '•  subtracted  from  a  equals  a-\-c 

The  Method  of  Leibnitz  would  solve  the  last  problem  thus:  a—a-\-c — c, 
and —(■  subtracted  from  a -(-c- — c  equals  a-f-c.  This  cannot  be  applied 
conveniently  to  the  problems  given  above.  The  method  of  adding  to 
both  terms  is  as  follows  :  adding  c  to  a,  we  have  a-\-c  ;  adding  c  to  — c 
we  have  c — c=0;  and  0  subtracted  from  a-\-c  leaves  a+c;  hence,  since 
the  difference  between  two  quantities  equals  the  difference  between  the  two 
quantities  equally  increased, —c  suhtTSiCted  from  a  leaves  a  I- c.  By  tbe 
method  of  Latitude  and  L»n;/itude,  we  consider  7a  as  representing  so 
many  degrees  north  of  the  ccjuator,  and  — 4a  as  representing  so  many 
degrees  «o«^A  of  the  equator;  and  the  difference  betw,  en  7a  north  and 
4a  south  is  evidently  7a+ 4"  or  11a.  It  is  not  so  fotf  enient  in  this 
method,  howt  ver,  to  fix  the  sijjn  of  the  difference.  Tlie  general  case 
may  be  explained  by  subtracting  b—c  from  a. 

6.  MHltipUcatio}! Multiplication  is  coii\eniently  treated 

under  two  cases:  \.  Tq  ffiiUtiply  by  a  monomial;  2.  To  multi- 


TEACHING    ALGEBRA.  445 

ply  by  a  polynomial.  In  presenting  multiplication,  there  luv 
four  things  which  require  attention:  1.  The  Co-efficients;  2. 
The  Literal  Part ;  3.  The  Exponents ;  4.  The  Signs.  To  ex- 
plain the  multiplication  of  the  co-efficient  and  the  literal  part, 
let  the  pupil  see  clearly  the  principle,  Maltiplying  any  factor 
of  a  quantity  multiplies  the  quantity.  To  explain  the  expo- 
nents, show  that,  The  exponent  of  a  term  in  the  product 
equals  the  sum  of  its  exponents  in  the  factors. 

Methods. — There  are  two  methods  of  explaining  the  signs. 
called  the  3Ionomial  Method  and  the  Binomial  Method.  The 
Binomial  Method  explains  by  multiplying  a—b  by  c—d;  and 
has  usually  been  emplo3'ed  by  mathematicians.  The  Mono- 
mial Method  is  preferable,  however,  as  it  looks  the  difficulty 
squarely  in  the  face,  and  shows  just  why  the  signs  should  be 
as  they  are. 

Illustration. — To  determine  the  law  of  the  signs,  we  will  multiply  h 
by  a  ;  —b  by  a  ;  b  by  —a ;  and  — b  by — a. 

First,  -\-b  taken  any  number  of  times,  operation. 

as  a  times,  is  evidently  -\-ub.  i  "        "      1"        " 

Second,  —b  taken  once  is  —b ;  taken 


twice,  is  -3/>,etc.;  hence,-6,  taken  any         +"^  ~^*  ~^^   ~+a? 
number  of  times,  as  a  times,  is — ab. 

Third,  b  multiplied  by  — a,  means  that  b  is  to  be  taken  subtractively  a 
times;  b  taken  a  times  is  nb,  and  taken  subtractively  is  —ab. 

Fourth,  —b  multiplied  by  —a,  means  that  —b  is  to  be  taken  subtract 
ively  a  times  ;  —b  taken  a  times  is  —ab,  and  used  subtractively  is  — ( — ab), 
which,  by  the  principles  of  subtraction,  is  -\-ab. 

Hence,  we  infer  that  t?ie  product  of  quantities  having  like  signs  is  PLUS, 
and  having  unlike  sigreg  is  minus. 

1.  Division. — Division  is  conveniently  treated  under  two 
cases:  1.  To  divide  by  a  monomial;  2.  To  divide  by  a  poly- 
nomial. There  are  four  things  to  be  considered,  as  in  multi- 
l>lication:  1.  The  Co-efficients;  2.  The  Literal  Part;  3.  The 
Exponents;  4.  The  Signs.  The  explanation  of  the  division 
of  the  co-efficients  and  letters  depends  on  the  principle, 
Taking  a  factor  out  of  a  quantity  divides  the  quantity  by  that 
factor.     The  explanation  of  the  exponents    depends  on  tlu" 


446  METHODS   OF   TEACHINQ. 

principle,  The  e.^  portent  of  a  term  in  the  quotient  equals  ith 
*',xponent  in  the  dividend  minus  its  exponent  in  the  divisor. 
Tlie  law  of  the  fi^ns  is  derived  from  the  law  of  the  sioriis  in 
multiplication. 

8.  Coinposition  and  Factorituj — For  the  treatment  of 
Composition  and  Factoring,  see  the  author's  Elementary 
Algebra.  Attention  is  called  especiall}-  to  the  demonstration 
of  the  theorem  concerning  the  divisibility  of  a" — 6"  by  a — 6, 
and  theorems  siaiilar  to  it.  The  usual  method  is  that  of  mnlhc- 
viatical  induction;  the  method  we  have  given  is  much  simpler. 
It  is  suggested  chat  the  student  be  thoroughly  drilled  in  Fac- 
toring, as  it  lies  at  the  basis  of  algebraic  analysis.  The 
student-teacher  may  be  required  to  give  an  outline  of  the 
several  cases,  and  show  how  to  teach  them. 

9.  Fractiona — Fractions,  in  algebra,  are  to  be  regarded  as 
the  expression  ol  one  quantity'  divided  by  another.  The 
principles  are  established  by  demonstration,  and  then  are  to 
be  applied  in  deriving  the  rules  of  operation.  Let  the  student- 
teacher  give  an  outline  of  the  cases,  and  explain  the  method 
of  their  treatment.  Show  also  what  difficulties  pupils  usuallj- 
meet  with,  and  how  to  explain  them. 

10.  Equations. — Tlie  elements  of  equations  are  simple  and 
readilv  taught.  Some  teachers  illustrate  transposition  by  a 
pair  of  scales  or  balances,  showing  that  if  anything  is  put 
into  or  taken  from  one  scale  an  equal  quantity  must  be  i)ut 
into  or  taken  from  the  other  scale.  Such  an  illustration  is 
not  needed,  however,  as  a  pupil  readily  gpsps  the  axiom  that 
if  equal !i  be  added  to  or  taken  from  equals,  the  results  will  be 
equal.  The  pupils  should  be  thoroughly  drilled  on  the  solu- 
tion of  equations  until  they  are  familiar  with  the  general 
methods  and  all  the  special  artifices  that  appl^-  to  particulai 
cases. 

11.  Solution  of  Problems. — Pupils  should  have  an  extensive 
drill  on  the  solution  of  concrete  problems.  The  solution  of 
such    problems    consists    of  two  parts;  the   forming    of  the 


TEACHING    ALGEBRA.  447 

equation,  and  the  solution  of  the  equation.  The  first  is  called 
the  concrete  part,  the  latter  the  abstract  part  of  the  solutioi;. 
The  pupil  should  have  wide  and  extensive  experience  in  hotl> 
of  these,  for  it  is  only  in  this  way  that  he  can  become  a  skill- 
ful algebraist.  He  maj'-  also  be  encouraged  to  make  new 
problems  for  himself  and  schoolmates  to  solve. 

General  Suggestions. — We  close  the  subject  with  soii;c 
general  su22:estions  to  the  teacher. 

Literal  Notation The  teacher  should  be  careful  to  see- 
that  the  pupils  have  a  clear  idea  of  the  literal  notation.  First, 
they  should  see  clearl}'  that  a  letter  represents  a  general  num- 
ber, and  that  this  number  may  be  integral  or  fractional. 
Second,  that  as  involved  in  an  expression,  each  letter  is  a 
factor.  There  should  be  a  drill  with  figures,  as  3x4x5,  and 
then  changing  to  a x6xc,  and  then  to  a6c,  until  this  idea  is 
clearly  developed. 

Positive  and  Xi^yative. — The  pupil  should  be  led  to  a  clear 
idea  of  the  positive  and  ?ie9a<it'e  quantities.  He  should  first 
be  taught  that  +  and  —  denote  operations.  He  should  next 
see  that  they  give  character  to  quantities,  and  indicate  posi- 
tive and  negative  quantities.  He  should  then  be  led  to  under- 
stand that  they  may  be  used  to  represent  quantities  reckoned 
in  opposite  directions. 

Exponents. — The  pupil  should  first  learn  to  use  and  under- 
stand exponents  as  indicating  the  powers  of  quantities.  After 
he  has  reached  the  idea  of  generalization  in  algebra,  he  should 
see  that  in  a^  ,  the  n  being  general  may  be  integral  or  frac- 
tional, and  that  when  fractional  the  numerator  denotes  a 
power,  and  the  denominator  a  root.  Again,  since  n  is  general 
it  may  be  negative^  and  as  such  needs  an  interpretation,  tiie 
origin  and  meaning  of  which  should  be  clearly  shown.  And, 
again,  n  being  general,  a'*  maybe  a°  or  a^ ,  each  of  which 
should  be  clearl}-  interpreted.  The  use  of  fractional  exponents 
in  radicals  should  be  thoroughly'  understood,  and  the  pupil 
should  be  taught  to  work  radicals  largely  through  fractional 


44S  METHODS   OF   TEACUINQ. 

exjMments.  This  will  simplify  man^^  points  tliat  are,  at  first, 
quite  difficult  for  the  learner. 

Generalization. — The  pupil  should  be  thoroughly  drilled 
in  the  generalizations  of  the  science.  The  spirit  of  generali- 
zation lies  at  the  basis  of  algebra,  and  no  one  can  understand 
it  until  he  is  thoroughly  imbued  with  this  spirit.  Pupils 
.should  be  required  to  generalize  special  problems  and   derive 

general  rule.  They  should  discuss  these  general  expres- 
sions, show  the  cases  that  ma}-  arise  for  different  suppositions, 
and  apply  these  expressions  in  the  solution  of  problems  of  a 
given  class. 

Interpretation. — The  pupil  should  be  trained  to  interpret 
algebraic  results.  The  solution  of  the  general  simple  equa- 
tion, ax — bx=c,  the  problem  of  the  couriers,  etc.,  should  be 
discussed,  and  the  different  results  which  arise  be  interpreted 
The  discussion  of  the  roots  of  the  general  quadratic  equation, 
x^-\-2px=q,  showing  the  relations  of  p  and  q  to  the  roots,  is 
a  most  valuable  exercise,  and  tends  to  imbue  the  mind  of  the 
pupil  with  the  true  algebraic  spirit.  Xo  one  is  an  algebraist 
who  cannot  interpret  results ;  and  a  knowledge  of  its  applica- 
tion to  the  physical  sciences  is  impossible  witho"*"  the  ability 
to  discuss  and  interpret  general  formulas. 


PHYSICAL  SCIENCE. 


CHAPTER  I. 


NATURE   OF   PHYSICAL   SCIENCE. 

nillE  Physical  Sciences  are  the  sciences  which  treat  of  the 
JL  material  world.  They  consist  of  facts  and  phenomena, 
and  the  truths  and  principles  which  relate  to  them.  They 
begin  in  tlie  observation  of  facts,  these  facts  are  classified, 
and  the  causes  which  produce  them  and  laws  which  control 
them  are  ascertained. 

The  object  of  these  sciences  is  the  interpretation  of  the 
physical  univei'se.  They  assume  that  man  is  the  interpreter 
of  nature,  and  that  science  is  its  right  interpretation.  They 
are  based  on  the  uniformity  of  nature,  and  thus  give  foresight 
to  man  and  enable  him  to  predict  what  will  take  place  in  the 
future.  The  scientist  thus  makes  prevision^  or  the  prophetic 
nature  of  knowledge,  the  basis  and  test  of  science.  Reason- 
ing from  the  standpoint  of  the  physical  sciences,  Herbert 
Spencer  defines  all  science  as  merely  tlie  power  of  prevision. 

I.  Classification. — No  complete  classification  of  the  phys- 
ical sciences  has  yaX,  been  given  which  is  satisfactory.  They 
so  overlap  and  interlace  that  it  is  difficult  to  draw  a  clearlj' 
marked  line  of  distinction  between  them.  The  principal 
branches  are  Natural  History,  Natural  Philosophy,  Astrono- 
my, Chemistry,  Geograph3%  Geology,  Biology,  etc.  These 
branches  are  distinguished  partly  b}^  their  subject  matter  and 
partly  by  their  objects  and  methods  of  development. 

(449) 


4-50  METHODS   OF   TEACHING, 

Natural  History Natural   History   treats  of  the  throe 

kin2:(loms  of  nature, — the  mineral,  the  veiretable,  and  the 
animal  kingdoms.  Its  object  is  to  ascertain  the  facts  relating 
to  the  nature,  structure,  and  growth  of  tlie  individual  objects, 
and  to  arrange  these  objects  in  scientific  classes.  It  assumes 
that  they  were  created  after  great  pattern  ideas,  and  that  iIk' 
object  is  to  discover  these  ideas  in  their  development,  and  to 
classify  accordingly.  They  have  been  appropriately  calle<l 
the  Classificatory  Sciences.  The  grand  object  of  Natuml 
History,  therefore,  is  classification. 

The  branches  of  Natural  Histor}^  are  Zoologj^,  Botany,  and 
Mineralogy.  In  Zoolosry  it  is  assumed  that  the  animal  kinor- 
dom  was  created  after  four  great  leading  ideas  or  types  of 
structure,  called  Vertebrates,  Articulates,  Radiates,  and 
Mollusks;  and  that  these  ideas  are  difierentiated  all  the  way 
down  to  species  and  individuals.  In  Botany  two  great  lead- 
ing types  are  found,  the  Phienogamia  and  Cryptogamia,  each 
of  which  constantly  divides  into  subdivisions,  ending  at  last 
in  species  and  individuals.  Mineralog}^  is  also  regarded  as 
the  development  of  ideas  which  form  distinctl}'  marked 
classes. 

Natural  Pliilosophy. — Natural  Philosophy  treats  of  the 
facts  and  phenomena  of  the  material  world.  Its  object  is  to 
ascertain  these  fiicts  and  phenomena,  and  to  discover  the 
causes  which  produce  them  and  the  laws  which  govern  them. 
Thus,  in  respect  to  falling  bodies,  it  ascertains  the  cause  to  be 
gravity ,  a.\\d  the  law  that  the  distances  are  proportioned  to  the 
squares  of  the  times.  It  seeks  to  acquire  the  facts  respecting 
Light,  to  explain  these  facts  by  the  cause  of  nndulatory 
motions,  and  to  discover  the  laws  of  reflection,  refraction,  etc. 
It  differs  from  Natural  History  in  that  its  facts  do  not  admil 
of  classification  into  genera  and  species;  and  also  in  that  it 
deals  more  particularly  with  laws  and  causes. 

The  principal  branches  of  Natural  Philosophy  are  Meclmn- 
ics,  Hydrostatics,  Pneumatics,  Optics,  Acoustics,  Thermotics, 


NATURE   OF   PHYSICAL   SCIENCE.  451 

etc.  Mechanics  treats  of  the  general  laws  of  force ;  IIy<lro- 
statics  treats  of  liquids;  Pneumatics  treats  of  the  air;  Oj^tics 
treats  of  light;  Acoustics  treats  of  sound;  Thermotics  treats 
of  heat;  etc.  These  divisions  seem  quite  distinutl}'  marked, 
and  yet  there  are  indications  of  future  changes;  and  even  the 
term  Natural  Philosophy  may  not  be  always  used  to  include 
the  several  branches  above  named. 

Astronomy. — Astronom}^  treats  of  the  facts  and  truths  re- 
lating to  the  heavenly  bodies.  It  is  closely  related  to  Natural 
Philosophy,  differing  mainly  in  the  subject  matter  of  its  in- 
vestigations. It  explains  the  appearances,  changes,  motions, 
etc.,  of  the  heavenly  bodies,  calculates  their  size  and  distance, 
investigates  their  composition,  structure,  etc.  It  is  appropri- 
ately named  the  "  sublime  science,"  and  gives  us  the  grandest 
ideas  of  the  nature  and  magnitude  of  the  physical  universe. 

Chemistry. — Chemistry  treats  of  the  nature  and  properties 
of  the  elements  of  bodies.  It  differs  from  Natural  Philos- 
ophy in  that  the  former  considers  the  general  laws  of  matter 
in  the  forms  in  which  it  presents  itself,  while  Chemistry  con- 
siders the  eleruents  out  of  which  matter  is  composed,  and  ex- 
plains the  changes  tliat  occur  in  bodies  through  the  operation 
of  these  elements.  Its  object  is  to  ascertain  the  composition 
of  material  things,  and  to  explain  the  method  of  their  forma- 
tion. It  regards  matter  as  composed  of  infinitely  small  ele- 
ments called  atoms;  and  thus  occupies  about  the  same  place 
among  the  physical  sciences  that  the  infinitesimal  calculus 
does  in  the  mathematical  sciences. 

Biology. — Biology  is  the  science  which  treats  of  life,  or 
living  matter.  It  seeks  to  ascertain  the  facts  and  understand 
the  laws  of  tlie  life  principle  found  in  matter,  and  endeavors 
to  explain  the  complicated  phenomena  of  living  beings.  It 
rises  above  the  other  natural  sciences  in  that  it  treats  not  only 
of  matter,  but  of  organized  matter;  it  considers  not  merely 
force,  but  that  life  force  which  holds  matter  in  its  hand,  and 
shapes  it  into  the  organic  beings  of  the  vegetable  and  animal 


452  METHODS   OF   TEACHING. 

world.  It  is  a  science  of  recent  development;  and  though 
difficult,  and  still  in  an  incomplete  condition,  is  one  of  great 
interest,  and  promises  to  be  of  great  practical  value.  There 
are  several  other  branches  of  the  Physical  Sciences,  as  Geol- 
ogy, Geography,  etc. 

II.  Elements  of  Physical  Science. — The  several  elements 
of  the  Physical  Sciences  are  Facts  and  Phenomena,  Systems 
of  Classification,  Causes  of  Facts  and  Phenomena,  Laws 
governing  Facts  and  Phenomena,  and  Truths  growing  out  of 
them.  The  object  of  the  inquirer  in  these  sciences  is  to  at- 
tain these  elements. 

Facts  and  Phenotnena. — The  primary  elements  of  the 
Physical  Sciences  are  Pacts  and  Phenomena.  A  Fact  is 
something  that  is  or  has  been.  It  is  a  particular  truth  in  the 
domain  of  sense.  It  is  something  seen  or  heard,  or  that  was 
revealed  through  one  of  the  senses.  It  is  confined  to  the 
present  or  the  past,  and  does  not  reach  out  to  the  future,  as 
that  is  the  sphere  of  a  truth.  Thus  it  is  a  fact  that  "the  sun 
rose  this  morning,"  that  "there  was  snow  last  winter,"  that 
water  freezes  at  32^  above  zero,"  etc.  A  Phenomenon  is 
literally  an  appearance;  as  the  twinkling  of  a  star,  the  chang- 
ing of  the  moon,  the  rising  of  the  tide,  etc.  The  statement 
of  a  phenomenon  in  a  proposition  gives  us  a  fact. 

Classifications. — Several  of  the  Physical  Sciences  aim 
especially  at  the  classification  of  facts.  In  Natural  History 
the  principal  elements  are  facts  and  their  classification.  In 
these  sciences  it  is  assumed  that  the  world  was  constructed 
after  great  pattern  ideas  or  plans  of  structure;  and  objects 
are  classed  by  means  of  these  ideas.  Zoolog}'  embraces  all 
the  animals  under  five  great  divisions ;  Branches,  Classes, 
Orders,  Families,  Genera,  and  Species.  The  Branches  repre- 
sent the  plan  of  structure;  the  Classes,  the  manner  of  execu- 
tion; the  Orders,  the  comparative  complication  of  execution; 
the  Families,  ditferences  of  form;  Genera,  details  of  structure; 
Species,  difference  in  size,  habits,  etc.     The  great  divisions  in 


NATURE   OF   PHYSICAL   SCIENCE.  453 

Botan}'  are  Species,  Genera,  Orders,  Cohorts,  Classes,  and 
Sub-kingdoms;  divisions  founded  in  nature,  and  thus  called 
the  Natural  System. 

C'nises. — The  grand  aim  of  the  Physical  Sciences  is  to 
ascertain  the  Causes  of  things.  B}"^  a  Cause  is  meant  that 
which  produces  an  event,  or  but  for  which  some  event  would 
not  occur.  The  great  question  of  Physics  is  why ;  and  the 
answer  to  this  question  gives  us  a  large  body  of  scientific 
truths.  Thus,  gravity  explains  why  a  stone  falls,  and  also 
the  planetary  motions  ;  the  earth  revolving  on  its  axis  ex- 
plains the  phenomena  of  day  and  night ;  elliptical  orbits  with 
the  sun  in  a  focus  explain  the  changes  of  the  heavenly  bodies; 
the  undulations  of  an  ethereal  fluid  explain  the  interesting 
phenomena  of  light,  etc.  These  causes  are  reached  through 
hypothesis  and  theory. 

Latvs. — The  second  great  aim  of  the  Physical  Sciences  is 
to  ascertain  the  Laws  of  physical  phenomena.  By  Laws  we 
mean  the  regular  mode  or  order  according  to  which  something 
operates  or  events  take  place.  This  element  is  closely  related 
to  the  inquiry  for  the  Cause,  but  yet  is  different  from  it.  Thus, 
gravity  is  the  cause  of  a  body  falling, but  it  is  a  law  that  the 
force  of  gravity  varies  inversely  as  the  square  of  the  distance^ 
or  that  the  distances  passed  over  by  a  falling  body  are  in  pro- 
portion to  the  squares  of  the  times.  The  cause  of  the  changes 
of  the  planetar}'^  bodies  is  an  elliptical  orbit;  and  a  law  of  mo- 
tion in  such  an  orbit  is  that  the  radius  vector  passes  over 
equal  areas  in  equal  times. 

Truths. — A  Truth  of  physical  science  is  a  statement  of 
some  established  principle,  or  some  inference  derived  from  it. 
Truths  embrace  both  laws  and  causes,  the  statement  of  a  law 
or  a  cause  being  a  truth.  The  statement  of  any  general  pro- 
position which  has  been  verified,  or  any  inference  derived  from 
it,  is  also  a  truth.  Thus,  heat  expands  all  metals,  or  there 
will  be  a  total  eclipse  of  the  sun  during  such  a  year,  are  also 
truths.  The  truths  of  physical  science  are  mainly  derived  i)y 
inductive  reasoning,  and  enable  us  to  predict  the  future. 


454  METHODS    OF   TEACHING. 

III.  How  Developed. — The  Ph3'sical  Sciences  begin  in  the 
common  observations  of  mankind.  This  common  knowledge 
is,  by  the  power  of  thought,  gradually  transformed  into  scien- 
tific knowledge.  Through  the  operation  of  the  natural  laws 
of  mental  activity,  the  common  knowledge  of  the  race  is  con- 
stantly rising  up  into  the  higher  and  more  perfect  forms  of 
science.  The  several  elements  that  enter  into  their  develop- 
ment, are  Observation  and  Experiment,  Classification,  Induc- 
tion, Deduction,  Hypothesis,  and  Theor}'. 

Observation — Observation  has  reference  to  the  perception 
of  nature  as  she  presents  herself  to  our  view.  By  it  facts 
and  phenomena  are  presented  to  the  mind  through  the  senses, 
and  are  then  retained  in  the  memory-  for  future  use.  In  sci- 
ence, this  observation  needs  to  be  careful  and  exact;  mere 
looking  or  listening  is  not  sufficient,  we  must  look  and  listen 
with  the  eye  of  reason.  Observation  must  be  made  with 
patience,  and  sources  of  error  must  be  guarded  against.  It 
must  also  be  analytic;  facts  and  phenomena  must  beanal3-zed, 
things  must  be  separated  or  broken  up  into  fragments  in  order 
that  the  information  may  be  minute  and  accurate.  Man  also 
invents  instruments,  as  the  microscope  and  telescope,  to  aid 
the  senses  in  observation,  and  thus  acquire  facts  which  he 
could  not  otherwise  obtain. 

Experiment. — B}'  Experiment,  man  puts  nature  into  new 
relations  to  observe  the  results.  He  not  only  observes,  but 
he  prepares  his  facts  for  observation.  Objects  are  placed  in 
different  relations  and  conditions,  and  the  changes  and  results 
noted  and  compared.  Nature  is,  as  it  were,  put  on  the  wit- 
ness stand,  and,  by  a  series  of  cross  questions,  forced  to  reveal 
her  secrets.  This  method  of  obtaining  facts  is  largely  used 
in  Natural  Philosophy,  au.d  in  Chemistry  it  is  in  constant  use. 

Classification. — As  facts  multiply,  the  mind  compares  them 
and  perceives  points  of  resemblance  between  them,  and  forms 
them  into  classes.  The  perception  of  the  similarities  and  dif- 
ferences is  an  act  of  Judgment  ;  tlie  separating  of  the  common 


NATQIIE    OF    PHYSICAL   SCIENCE.  455 

qualities  to  unite  tliera  into  a  general  scheme  is  abstraction, 
and  the  forming  of  the  general  class  idea  is  generalization 
The  arrangement  of   the  objects  themselves  into    classes  is 
calletl  clasiiification.     This  process  of  classification  is  neces 
sar^'  in  all    the   sciences;    but   it   is  especialh'  prominent  ir. 
Natural  History. 

Induction. — Induction  lies  at  the  basis  of  the  truths  ot 
the  Physical  Sciences.  Observation  and  Experiment  give 
ns  the  particular, facts  ;  Induction  takes  these  facts  and  finds 
the  laws  which  contain  or  control  them.  Thus  from  the  facts 
that  heat  expands  iron,  zinc,  copper,  etc.,  we  derive  by  In- 
duction the  general  truth  that  heat  expands  all  metals.  It  is 
this  process  of  thought,  so  generall}'  neglected  by  the  an 
cients,  and  made  so  prominent  in  the  Baconian  s^'stem,  that 
has  given  such  rapid  growth  to  the  ph3-sical  sciences  during 
the  last  century. 

Deduction. — The  method  of  Deductive  reasoning  is  also 
used  in  the  Physical  Sciences.  Having  reached  a  general 
conclusion  by  Induction,  we  apply  this  truth  to  new  facts  by 
a  process  of  Deduction.  Thus,  if  we  discover  a  new  metal, 
we  immediately  infer  that  heat  will  expand  it,  from  the  gen- 
eral principle  that  heat  will  expand  all  metals.  The  mathe- 
matician takes  the  doctrine  of  universal  gravitation,  puts  it 
into  an  equation,  and  works  out,  in  the  solitude  of  his  study, 
the  position  of  a  new  planet ;  and  the  telescope,  sweeping  the 
field  of  the  heavens,  discovers  the  wanderer,  and  thus  confirms 
"the  immortal  predictions  of  science."  It  is  thus  true  that 
"  Induction  discovers  principles,  while  Deduction  applies 
them  ;"  or  as  Tyndall  observes,  "In  the  stud}'  of  Phj-sics,  in- 
duction and  deduction  are  perpetually  married  to  each  other." 

Hypothesis. — The  Phj'sical  Sciences  are  aided  in  their 
development  by  Hypothesis.  An  Hypothesis  is  a  supposition 
to  account  for  facts  and  phenomena.  The  facts  are  presented 
through  the  senses,  and  the  mind  makes  some  supposition  to 
account  for  them.     Such   suppositions,  or   hypotheses,   have 


456  METHODS   OF   TEACHING. 

given  us  a  large  number  of  the  truths  of  the  physical  scien- 
ces. Nearly  all  their  great  truths  were  once  hj-potheses.  Kep- 
ler's law  of  elliptical  orbits  was  once  a  mere  hypothesis ;  he 
made  and  rejected  nineteen  before  he  discovered  the  true  one. 
Newton's  theory  of  gravitation  was  at  first  only  an  hj-pothe- 
sis ;  and  when  verified  became  an  accepted  truth. 

Verification — Having  formed  our  hypothesis,  the  next  step 
is  to  prove  it  to  be  true.  This  is  called  its  verification.  To 
verify  an  hypothesis,  it  must  be  shown  that  it  will  account 
for  all  the  known  facts  to  which  it  relates.  If  facts  are  found 
that  it  will  not  account  for,  another  supposition  must  be  made, 
and  so  on  until  one  is  obtained  that  is  correct.  Great  care, 
however,  must  be  taken,  not  to  accept  an  hypothesis  as  true 
until  the  fiicts  are  so  numerous  that  there  can  be  no  doubt  of 
its  verification.  "  To  tr\'  wrong  guesses,"  says  Dr.  Whewell, 
"is,  with  most  persons,  the  only  way  to  hit  upon  right  ones." 

Origin  of  Hypotheses. — The  hypotheses  of  science  origin- 
ate by  what  is  called  anticipation.  Anticipation  is  the  pre- 
saging of  a  truth  before  there  is  evidence  to  prove  it.  By  the 
power  of  anticipation  the  mind  leaps  from  a  few  facts  to  the 
law  which  governs  them.  All  hj'potheses  are  the  result  of 
what  La  Place  calls  a  "great  guess,"  or  of  what  Plato  so 
beautifully  designates  as  "a  sacred  suspicion  of  truth."  The 
forming  of  hypotheses  requires  a  suggestive  mind,  a  lively 
fancy,  a  philosophic  imagination,  that  cat-ches  a  glimpse  of  the 
idea  through  the  form,  or  sees  the  law  standing  behind  the 
fact. 

Theory. — The  Ph3'sical  Sciences  are  largely'  made  up  of 
Theories.  A  Theory  is  an  accepted  explanation  of  facts  and 
phenomena.  It  may  also  be  defined  as  a  verified  hypothesis. 
When  an  hj'pothesis  is  shown  to  explain  all  the  facts  that  are 
known,  these  facts  being  varied  and  extensive,  it  is  said  to  be 
verified,  and  becomes  a  theory.  Thus  we  have  the  theory  of 
universal  gravitation,  the  Copernican  theory  of  the  solar 
system,  the  undulatory  theory  of  light,  etc.,  all  of  which 
were  originally  mere  hypotheses. 


NATURE    OF   PHYSICAL   SCIENCE.  457 

lY.  Value  of  Physics. — The  importance  of  the  study  of 
the  physical  sciences  has,  until  recently,  been  largely  over- 
looked in  our  systems  of  education.  Language,  mathematics, 
and  the  metaphj-sical  sciences,  were,  for  many  years,  the  prin- 
cipal branches  of  a  collegiate  and  academic  course.  It  is  but 
recently  that  the  physical  sciences  have,  to  any  large  extent, 
been  introduced  into  the  curricula  of  our  higher  institutions; 
and  in  our  common  schools  thej'  are  still  almost  entirely 
omitted.  A  few  remarks  are  therefore  appropriate  concerning 
the  value  of  these  studies. 

1.  The  study  of  the  physical  sciences  gives  culture  to  the 
perceptive  powers.  The  physical  sciences  begin  in  the  ob- 
servation of  the  facts  of  the  external  world.  The  proper 
study  of  these  sciences  requires  the  pupil  to  observe  these 
facts  closely  and  accurately.  They  thus  call  the  perceptive 
powers  into  constant  and  forcible  activity ;  quicken  and 
strengthen  the  power  of  the  senses,  and  make  the  student 
shnrp-eyed  and  accurate  in  his  observation  of  things.  Among 
all  the  studies,  they  especially,  and  almost  alone,  give  culture 
CO  the  perceptive  powers. 

2.  The  study  of  the  physical  sciences  gives  culture  to  the 
power  of  classification.  The  facts  of  the  material  world  are 
created  in  classes,  and  the  natural  sciences  embrace  the  classi- 
fication of  the  facts,  as  well  as  the  facts  themselves.  These 
classifications,  in  several  of  the  branches,  are  the  most  perfect 
that  can  be  found  in  science.  The  arrangement  into  species, 
genera,  orders,  and  kingdoms,  as  in  botan\',  zoology,  etc.,  has 
no  counterpart  in  the  other  sciences.  The  natural  sciences, 
therefore,  transcend  all  others  in  affording  cultivation  to 
generalization  and  classification.  The^',  above  all  other  sci- 
ences, tend  to  train  the  mind  to  the  habit  of  the  sj'stematic 
and  orderly  arrangement  of  knowledge. 

3.  The  study  of  the  physical  sciences  cultivates  the  power 
of  inductive  reasoning.  All  the  primar}'  truths  of  these  sci- 
ences are  derived  by  induction.     In  their  stud}'  we  are  con- 

20 


i58 


METHODS    OF   TEACHING. 


stantly  passing  from  particular  facts  to  the  general  laws  of 
which  they  are  examples.  In  no  other  sciences  is  the  use  of 
induction  an3'thing  like  so  prominent.  Though  some  of  these 
sciences  may  rise  into  a  deductive  stage,  3'et  the  entire  spirit 
of  these  bi-anches  is  inductive.  Induction  is  the  genius 
which  presides  over  their  origin  and  development.  The  mind 
of  the  student  is  thus  constantly  occupied  in  inferring  general 
laws  from  particular  facts,  and  acquires  the  habit  of  reasoning 
in  this  way.  The  importance  of  such  culture  is  seen  in  the 
fact  that  this  is  the  kind  of  reasoning  that  we  use  in  the  ques- 
tions that  meet  us  in  the  ordinary  duties  of  life. 

4,  The  study  of  the  physical  sciences  tends  to  modify  the 
dogmatic  spirit  cultivated  by  the  deductive  sciences.  The 
study  of  the  deductive  sciences  tends  to  make  the  mind  over- 
bearing and  dogmatic.  The  pure  mathematician  is  as  stub- 
born as  a  mule,  in  his  belief.  Accustomed  to  see  certain  con- 
clusions flow  from  admitted  premises,  he  applies  the  same 
method  to  social  and  political  questions,  and  is  intolerant  of 
any  opposition  to  his  opinions.  Natural  science,  leading  the 
mind  by  the  path  of  inductive  thought,  accustoms  it  to  see 
bow  easy  it  is  to  be  mistaken  in  an  inference,  and  makes  it 
cautious  in  its  conclusions,  and  tolerant  of  doubt.  The  sci- 
entists are  the  most  modest  and  the  least  positive  in  their  be- 
liefs of  any  class  of  thinkers;  indeed,  many  of  the  points  of 
ditference  between  theology  and  science  are  the  inferences  of 
the  theologians  from  the  premises  of  science,  rather  than  the 
claims  of  the  scientists  themselves.  The  fact  that  the  path- 
way of  the  physical  sciences  is  strewn  with  the  remains  of 
discarded  theories,  is  sufficient  to  cultivate  a  spirit  of  mod- 
esty and  charity. 

5.  The  physical  sciences  have  contributed  to  the  development 
of  the  material  interests  of  mankind.  They  have  done  much 
to  lift  man  up  out  of  a  condition  of  barbarism  and  ignorance. 
They  have  enabled  him  to  improve  the  tillage  of  the  soil,  to 
raise  larger  and  better  crops,  to  lessen  and  lighten  his  labor. 


NATURE   OF   PHYSICAL   SCIENCE.  ^59 

to  establish  manufactories,  and  in  a  thousand  ways  have  min- 
istered to  his  comfort  and  convenience.  They  have  given  him 
machinery  by  which  he  can  multiply  his  strength  and  skill, 
and  do  that  which  his  unaided  powers  could  never  accomplish. 
They  have  built  his  houses,  covered  the  ocean  with  the  white 
wings  of  commerce,  laid  rails  to  carry  his  products  across 
wide  continents,  disseminated  education  by  the  invention  of 
the  printing  press,  and,  by  improving  his  material  condition, 
enabled  him  to  lift  himself  up  into  a  higher  civilization. 

Objections. — Though  the  physical  sciences  are  thus  valuable 
to  man,  there  are  objections  to  the  exclusive  study  of  these 
branches.  The  natural  tendency  of  such  study  is  to  lead  to 
materialism  in  thought  and  philosophy.  Accustoming  the 
mind  to  the  concrete,  they  unfit  it  to  comprehend  and  appre- 
ciate abstract  truth.  They  thus  tend  to  lower  the  tone  of 
man's  thought  and  sentiment,  to  destroy  the  imaginative  and 
poetic  in  literature,  to  take  the  divine  element  of  inspiration 
out  of  art,  and  to  weaken  the  religious  faith  of  mankind. 
Though  the  sciences  of  geology  and  astronomy  give  grand 
ideas  of  the  creation,  and  some  of  the  other  branches  afford 
evidences  of  a  marvelous  design  in  organic  life;  and  though 
some  scientists  have  said  that  "the  facts  of  the  world  are  the 
thoughts  of  God,"  yet  it  must  be  admitted  that  the  exclusive 
study  of  the  physical  sciences  leads  the  mind  naturally  to- 
wards a  hard,  dry  materialism,  which  has  no  place  for  the 
highest  aspirations  of  the  human  heart,  for  God,  Immortality, 
and  Heaven, 


CHAPTER  II. 

TEACHING   GEOGRAPHY. 

GEOGRAPHY  treats  of  the  facts  relating  to  the  surface  of 
the  earth.  It  seeks  to  describe  and  classify- these  facts, 
and  to  explain  their  causes  and  the  laws  which  control  them. 
The  term  Geography  is  derived  from  ge,  the  earth,  and 
grapho,  I  descril^e,  and  means  literally  a  description  of  the 
earth,  and  this  was  its  primary  sense. 

I.  Nature  of  Geography. — Geograph}-  is  not  so  much  a 
distinct  science  as  a  collection  of  facts  and  principles  drawn 
from  the  other  sciences.  In  its  widest  sense.  Geography  em- 
braces all  that  we  know  of  the  earth  ;  its  form,  size,  motions, 
structure,  present  and  past  condition,  products,  inhabitants, 
etc.  As  usually  treated,  it  runs  into  and  embraces  parts  of 
several  of  the  sciences,  as  astronomy,  botany,  zoology,  etc., 
though  it  has  a  sphere  of  its  own  somewhat  distinct  from  any 
of  these  other  branches. 

Division. — The  most  natural  division  of  Geography  seems 
to  be  into  Physical  and  Political  Geography.  Physical  Geog- 
raphy is  that  which  pertains  to  the  earth  in  its  natural  condi- 
tion, including  land,  water,  the  atmosphere,  the  climate,  and 
the  distribution  of  the  mineral,  vegetable,  and  animal  king- 
doms. Political  Geography  is  that  which  treats  of  the  earth 
as  modified  by  man, — its  countries, cities,  towns, and  inhabit- 
ants, including  their  customs,  religion,  government,  etc. 
Popularly,  however,  the  term  Physical  Geography  has  been 
used  to  include  the  philosophy  of  geography,  embracing  the 
generalizations  of  the  science  and  a  discussion  of  the  causes 
and  laws  of  geographical  phenomena. 

Besides  these  divisions,  writers  speak  of  Local  Geography, 

(460) 


TEACHING   GEOGRAPHY.  461 

Descriptive  Geography,  Mathematical  Geography,  Historical 
Geography,  etc.  All  of  these  have  a  special  meaning,  and  are 
convenient  in  instruction,  though  they  do  not  indicate  scien 
tific  divisions  of  the  subject.  The  division  which  comes  near- 
est the  present  actual  usage  is  that  into  Descriptive  and 
Physical  Geography' ;  the  former  treating  of  the  facts  of  geog- 
raphy, and  the  latter  of  the  laws  and  causes  of  geographical 
facts. 

Origin. — Geography  is  a  comparatively  modern  science. 
The  geographical  knowledge  of  the  ancient  Egyptians  and 
Phoenicians  was  confined  to  the  shores  of  the  Mediterranean 
Sea.  The  military  expeditions  of  Alexander,  in  the  fourth 
century  B.  C,  extended  the  knowledge  of  the  Greeks  consid- 
erably. Eratosthenes,  about  200  B.  C,  first  reduced  the 
geographical  knowledge  of  the  Greeks  to  a  scientific  form. 
Strabo  and  Ptolemy  wrote  treatises  upon  the  subject,  which 
contained  nearly  all  that  was  known  by  mankind  for  several 
centuries.  Prince  Henry  of  Portugal,  called  the  Navigator, 
added  considerably  to  this  knowledge  during  the  fifteenth 
centurj'.  The  discoveries  of  Columbus,  however,  opened  up 
a  new  world  and  gave  a  new  impetus  to  the  discover}^  of 
geographical  facts.  The  geographical  societies  of  France  and 
England  have  contributed  largely  to  geographical  knowledge 
durinoj  the  last  50  or  60  years. 

The  first  text-book  on  geography  published  in  this  country 
was  a  small  18mo.  manual  by  Jedediah  Morse,  issued  in  1784. 
This  was  the  principal  text-book  until  1822,  when  William  C. 
Woodbridge  and  Mrs.  Emma  Willard  issued  a  work  entitled 
The  Woodhridge  and  Willard  Geographies  and  Atlases.  In 
1823,  Sidney  E.  Morse  published  a  work  entitled  a  New  Sys- 
tem of  Modern  Geography,  which  was  several  times  revised 
and  had  a  wide  and  long  continued  circulation.  Some  of  the 
principal  writers  who  followed  Morse  were  Olnev,  Smith,  and 
Mitchell,  the  works  of  the  latter  author  being  especially  pop- 
ular. 


462  METHODS   OF   TEA-CHINQ. 

The  earliest  text-books  made  local  geograph}'-  very  promi- 
Dent,  some  works  containing  very  little  description.  In  in- 
struction, also,  the  description  of  geographical  facts  was  gener- 
ally neglected.  By  degrees  the  descriptive  part  became  more 
prominent,  both  in  text-books  and  in  instruction.  The  next 
step  in  advance  was  the  attempt  to  classify  the  facts  of  geog- 
raphy, and  to  present  their  laws  and  causes.  The  labors  of 
Humboldt  and  Ritter  in  this  respect  were  introduced  into 
this  country  by  Guyot  in  his  lectures,  and  in  a  work  entitled 
The  Earth  and  Man.  Several  works  were  soon  prepared  on 
Physical  Geography,  in  which  the  facts  were  classified  into 
systems  and  their  causes  and  laws  explained.  Recentlj'  at- 
tempts have  been  made  to  combine  this  with  the  local  and 
descriptive  geography  in  text-books  for  young  pupils  ;  but  not 
with  entire  success.  One  or  two  series  that  claimed  such  a 
combination  as  an  especial  merit,  were  found  not  to  work  well 
m  the  class-room,  and  had  to  be  revised  and  made  to  conform 
more  to  the  idea  of  presenting  the  facts  of  the  subject  before 
its  philosophy. 

II.  Methods  of  Teaching  Geography. — There  are  two  dis- 
tinct Methods  of  Teaching  Geography,  which  are  appropriately 
distinguished  as  the  Analytic  and  Synthetic  methods.  The 
anal^^tic  method  begins  with  the  world  as  a  whole  and  passes 
by  successive  division  down  to  the  state,  county,  and  town  or 
city,  in  which  one  resides.  The  synthetic  method  begins  at 
the  smaller  division  and  passes  by  successive  enlargements  to 
the  entire  surface  of  the  earth.  There  is  also  the  Inductive 
Method  which  begins  with  particular  facts  and  passes  to  their 
generalization  and  laws  ;  and  the  Deductive  Method  which 
begins  with  a  genei*al  view  of  geographical  facts  and  passes  to 
particulars.  Some  German  writers  speak  also  of  the  Con- 
structive Method ;  but  this  seems  to  be  a  mere  appendage  to 
the  other  methods,  and  not  a  distinct  method  of  itself. 

Synthetic  Method The  Synthetic  Method  begins  at  home 

and  passes  b}^  successive  additions  over  the  whole  globe.     It 


TEACHING   GEOGRAPHY.  463 

starts  with  the  school-house  and  yard,  takes  in  the  surround- 
ing farms,  then  passes  to  the  township,  the  county,  and  the 
state,  from  the  state  to  the  United  States  and  the  Western 
Hemisphere,  and  at  last  covers  the  entire  globe. 

Several  reasons  can  be  given  in  favor  of  the  synthetic 
method.  First,  it  seems  to  be  more  in  accordance  with  the 
principle, from  the  known  to  the  unknown,  as  it  passes  from 
the  familiar  things  around  us  that  we  can  see,  to  those  that  are 
distant  and  can  only  be  conceived.  Second,  the  pupil  thus 
first  gains  a  knowledge  of  the  geography  of  his  own  county 
and  state,  which  it  would  seem  is  of  more  importance  to  him 
than  a  knowledge  of  remote  countries  of  which  he  seldom 
hears  or  reads.  The  second  consideration  is  especially  im- 
portant if  the  time  for  the  study  is  restricted  or  accident- 
ally curtailed,  since  the  remote  parts  of  the  globe  would  thus 
be  omitted  rather  than  those  with  which  his  life  will  be  most 
closely  connected.  An  objection  to  the  method  is  that  the 
attempt  to  carry  it  out  strictly  and  completely  would  make 
the  course  very  tedious  or  lead  to  tiresome  repetitions.  A 
further  objection  is  that  the  mind  generally  prefers  to  operate 
analytically,  passing  from  a  general  view  of  the  whole  to  a 
detailed  consideration  of  its  parts. 

AnaljiUc  Method The  Analytic  Method  begins  with  the 

globe  as  a  whole  and  by  successive  divisions  passes  to  the 
various  parts  of  which  it  is  composed.  It  divides  the  earth 
into  land  and  water,  comes  down  from  the  continents  to  the 
countries,  states,  counties,  and  townships,  and  from  the  large 
bodies  of  water  to  the  smaller  ones.  This  method  is  the  reverse 
of  the  synthetic  method,  beginning  where  that  ends,  and  end- 
ing where  that  begins. 

There  are  several  reasons  in  favor  of  the  analytic  method. 
First,  it  admits  the  early  introduction  of  the  globe.  It  thus 
gives  a  more  correct  idea  of  the  relations  and  comparative 
size  of  the  different  countries,  and  prevents  some  of  the 
wrong    conceptions    that   inevitably    flow     from    the    othei 


464  METHODS   OF   T£aCHINQ. 

jiethod.  Second,  it  enaliles  us  to  present  earlier  the  astro- 
flomical  elements  of  geography  ;  such  as  the  changes  of  day 
and  night,  the  changes  of  the  season^.,  the  nature  and  the  use 
of  latitude  and  longitude,  etc.  Third,  it  follows  the  general 
law  of  acquisition, — from  the  whole  to  its  parts,  or  from  tlie 
larger  part  to  the  smaller  part,  instead  of  from  details  to  the 
whole. 

Inductive  Method The  Inductive   Method   begins  with 

the  particular  facts  of  the  science  and  passes  to  their  classifi- 
cation into  S3'stems.  It  is  in  spirit  the  method  by  which  the 
subject  has  been  taught  for  many  years,  although  until  re- 
cently the  course  did  not  pass  beyond  the  facts  of  the  subject. 
It  is  the  manner  in  which  it  is  noAv  ])resented  by  those  authors 
who  follow  their  work  in  descriptive  geography  by  a  work  on 
Physical  Geography.  To  carry  out  the  method  fully,  we 
should  begin  with  the  facts  of  geography  around  us  that  we 
can  perceive  before  we  learn  to  define  or  describe  them. 

Several  reasons  can  be  given  in  favor  of  the  Inductive 
Method  of  teaching  geography.  It  corresponds  with  the 
primary  law  of  mental  development,  from  the  particular  to 
the  general.  The  mind  naturally  learns  facts  Ijefore  it  learns 
to  classify  them  into  general  systems.  It  is  thus  much  easier 
than  the  deductive  method,  which  requires  the  grasp  of  a  gen- 
eral system  before  the  mind  is  familiar  with  details. 

Deductive  Method. — The  Deductive  Method  of  teaching 
geography'  begins  with  a  general  view  of  the  facts,  and  passes 
to  the  particulars  embraced  in  the  general  system.  It  seizes 
upon  the  laws  or  general  characteristics  of  a  group  of  facts, 
and  interprets  the  particular  facts  from  the  conception  of  the 
group.  Thus,  from  river  systems  it  passes  to  particular  river? 
from  mountain  S3'stems  to  individual  mountains,  from  fact^ 
that  stand  in  the  relations  of  cause  to  the  effects  which  they 
produce,  etc.  The  method  is  analytical  in  its  nature,  but  is 
more  than  analytic,  since  it  not  only  goes  from  the  whole  to 
its  parts,  but  from  the  general  to  the  particular. 


TEACHING    GEUGKAPiiy.  4(35 

There  are  several  advauta<^es  aud  disadvantasres  in  this 
method.  It  is  unsuitable  to  the  beginner,  as  it  inverts  the 
law  of  mental  development,  from  the  particular  to  the  gen- 
eral. It  is  not  surprising  that  the  recent  attempts  to  intro- 
duce it  into  our  elementary  text-books  on  geography  were  un- 
successful. It  is  of  great  value  to  the  advanced  student,  for 
it  aids  him  in  remembering  aud  understaudiusr  the  details  as 
he  sees  their  causes,  and  looks  at  them  through  their  relation 
to  a  general  scheme  or  law.  It  is  not  surprising  that  the 
method  when  first  presented  was  so  attractive  to  adult  minds, 
and  this  will  account  for  the  fact  of  the  enthusiastic  approval 
of  certain  text-books  which  did  uot  meet  expectation  in  the 
actual  work  of  the  school-room. 

III.  Courses  in  Geography. — There  should  be  three  distinct 
coui'ses  in  teaching  geography.  First,  there  should  be  a 
course  of  lessons  for  beginners,  giving  the  general  ideas  and 
facts  of  the  subject;  second,  there  should  be  the  detailed 
stud}'  of  geographical  facts;  and  third,  there  should  be  a 
course  in  the  philosophy  of  geograi)h3'.  The  first  course  may 
be  called  Primary  or  Elementary'  Geography;  the  second, 
Descriptive  Geography;  the  third,  Physical  Geograph3\ 

Pritnary  Geogruphy. — The  primary  course  in  geography 
includes  the  leading  ideas  and  fiicts  of  local  and  descriptive 
geography.  It  is  designed  to  present  to  children  their  funda- 
mental knowledge  of  the  subject.  The  instruction  should  be 
given  orally  in  connection  with  illustrations,  the  globe,  and 
outline  maps,  the  pupils  not  being  required  to  study  the  sub- 
ject from  a  text-book. 

The  primary  course  embraces  several  distinct  stages:  first, 
Si  perceptive  stage ;  second,  a  conceptive  stage;  third,  a  repre- 
sentative stage;  and  fourth,  an  explanatory  stage.  The  first 
and  second  of  these  stages  shouhl  be  most  prominent  in  the 
primary  course;  but  the  elements  of  the  representative  and 
explanatory'  stages  are  also  to  be  presented. 

Descriptive  Geography. — The  second  course  embraces  a 
30* 


4:QS  METHODS   OF    TEACHING 

detailed  description  of  the  facts  of  geography.  These  facta 
are  to  be  learned  from  text-books,  and  presented  by  the  pupils 
in  topical  recitations.  It  is  a  detailed  course  in  descriptive 
and  local  geography,  following  the  attainment  of  the  funda- 
mental ideas  given  in  the  primary  course.  It  combines  both 
the  analytic  and  synthetic  methods  of  treatment,  but  employs 
principally  the  analytic. 

Physical   Geographxj The   third    course    includes    the 

classification  of  the  facts  of  geography  into  systems,  and  also 
the  discussion  of  the  causes  of  geographical  phenomena,  and 
the  laws  which  govern  them.  It  is  the  philosophical  stage, 
and  has  been  treated  by  American  authors  under  the  head  of 
Physical  Geography. 

I.  Teaching  Peimary  Geography. 

The  course  in  Primary  Geograi)hy  includes  that  elementary 
instruction  which  imparts  the  fundamental  ideas  and  facts  of 
the  science.  It  embraces  four  distinct  stages;  the  Perceptive, 
the  Conceptive,  the  Representative,  and  the  Explanatory 
stages.  We  shall  first  speak  of  the  Principles  of  Instruction 
in  tliis  course,  and  then  show  the  Methods  of  Teaching  in  each 
one  of  these  four  stages. 

I.  Principles  of  Teaching. — There  are  several  general 
principles  which  should  guide  us  in  teaching  primary  geog- 
raphy. These  principles  may  seem  very  simple;  but  they 
have  been  constantly  violated  by  teachers,  and  even  by  those 
who  were  regarded  as  intelligent  and  successful  instructors 
of  the  branch. 

I.  The  course  of  instruction  in  primary  geography  should 
be  given  in  the  concrete.  The  geographical  ideas  should  be 
presented  to  the  mind  of  the  learner  by  illustration,  rather 
than  by  description.  This  can  be  done  by  showing  the  ob- 
jects in  nature,  or  b}-  having  models  of  them  or  j^ictures  of 
them.  When  it  is  possible,  the  pupils  should  be  shown  the 
physical  features;  as  a  mountain,  river,    lake,    island,    cape. 


TEACHING   GEOGRAPHY.  467 

isthmus,  peninsula,  etc.  Man}-  of  these  can  be  seen  in  mini- 
ature in  nearly  every  neighborhood.  We  may  go  out  by  the 
riverside,  or  even  by  the  side  of  a  small  stream,  and  studj- 
geography.  To  take  the  pupils  out  into  the  yard  after  a  rain 
and  study  geography  in  a  ''  mud  puddle,"  would  be  bettei 
than  the  ordinary  abstract  methods  of  the  school-room. 

Good  pictures  of  these  objects  will  also  be  valuable  in  lead- 
ing pupils  to  clear  conceptions  of  them.  The  so-called  "geo- 
graphical box,"  or  what  is  still  better,  the  modeling  in  sand  on 
the  "moulding  board,"  will  be  found  very  useful  with  beginners 
in  geography.  The  apparatus  found  at  our  late  Centennial  Ex- 
hibition indicate  European  methods  of  teaching  geography,  and 
are  worthy  of  our  imitation. 

2.  The  course  of  instruction  in  primary  geography  should 
be  first  synthetic  and  then  analytic.  We  should  begin  geog- 
raphy at  home,  in  the  school-house  and  yard.  From  this  we 
should  go  out  to  the  surrounding  fields  and  neighborhood. 
A  short  course  on  the  map  of  the  township,  county,  and 
state  ma}-  be  given.  We  should  then,  and  perhaps  earlier,  pass 
to  a  conception  of  the  world  as  a  whole,  and  study  it  ana- 
lytically. We  first  separate  the  surface  into  the  two  great 
divisions,  land  and  water;  then  come  down  from  the  conti- 
nents to  countries,  states,  counties,  and  townships.  Tlius, 
though  we  should  begin  witli  the  synthetic  method,  we  should 
be  careful  not  to  continue  it  too  long,  as  the  pupil  will  study 
the  subject  much  more  satisfactorily  by  the  analytic  method 
than  by  the  sj-nthetic  method. 

3.  The  course  of  instruction  in  primary  geography  should 
present  facts  before  giving  their  classification  and  causes. 
This  i)rinciple  is  in  accordance  with  the  natural  laws  of  mental 
acquisition.  It  accords  also  with  the  historical  order  of  the 
development  of  the  science.  The  facts  of  the  science  were 
known  long  before  their  classification.  Physical  Geography, 
as  presented  in  our  text-books,  is  much  more  recent  than 
Descriptive  Geography.     The  attempt  to  invert   this   order, 


468  METHODS   OF   TEACHING. 

which  has  been  made  in  some  of  our  recent  text-books,  wab  a 
mistake;  and  it  is  no  wonder  that  the  books  needed  early  re- 
vision. The  facts  of  local  and  descriptive  geography  must 
precede  the  attempt  to  generalize  these  facts  into  a  system. 
There  must  be  some  knowledge  of  the  individual  rivers, 
mountains,  etc.,  before  a  pupil  is  prepared  to  appreciate  river 
systems,  mountain  systems,  etc. 

4.  The  course  of  instruction  in  primary  geography  should 
begin  with  local  and  descriptive  geography.  The  child  is  in- 
terested in  and  can  readily  understand  and  remember  local 
geography.  He  carries  in  his  mind  the  picture  of  the  map 
and  the  location  of  places,  rivers,  etc.,  and  has  little  ditficultj' 
in  remembering  their  names.  To  restrict  the  pupil,  however, 
to  local  geography,  as  is  too  often  done,  is  a  mistake.  The 
t-eaching  of  mere  names  and  places  is  a  waste  of  time,  for  a 
large  number  must  necessarily  drop  out  of  the  memory.  The 
drilling,  day  after  day,  upon  "  map  questions"  without  any 
description,  is  of  little  value  to  pupils. 

The  description  of  places  should  be  joined  to  the  location 
of  places.  Interesting  facts  should  be  associated  with  the 
locations,  for  they  will  not  only  be  of  value  themselves,  but 
aid  in  fixing  the  location  in  the  memory.  That  which  was 
merely  a  "  spot  on  the  map"  with  a  name,  becomes  a  living 
reality  to  the  pupil  when  interesting  facts  are  associated  with 
it.  These  facts  may  be  given  and  then  the  place  located  ;  or 
we  may  pass  from  the  location  to  the  descrii)tion.  In  prac- 
tice, the  latter  method  will  be  usually  found  more  convenient. 
Local  geography  may  thus  precede,  but  it  shouM  carry  with  it 
descriptive  geography.  After  locating  a  country  and  point- 
ing out  its  principal  cities,  rivers,  etc.,  the  te;iclier  should  give 
and  then  require  a  description  of  its  striking  features,  of  its 
important  events,  of  its  people,  their  habits,  emph^yments,  etc. 

5.  2Vie  course  of  instruction  in  primanj  geography  should 
include  hiMorical  geography.  In  teaching  geography,  the 
leading  historic  events  should  be  associated  with  the  places 


TEACHING   GEOGKAPHY.  469 

described.  As  we  describe  the  different  countries,  reference 
may  be  made  to  the  leading  events  of  their  histor3\  In  con- 
nection with  tlie  geograpliy  of  the  Old  World,  facts  concern- 
ing Cyrus,  Xerxes,  Alexander,  C.Bsar,  Charlemagne,  Alfred, 
Wallace,  Bruce,  Napoleon,  the  Crusaders,  the  Spanish  Arma- 
da, etc.,  may  be  related.  In  considering  the  Western  Conti- 
nent, the  story  of  its  discover^^  the  course  of  the  vessels,  the 
place  of  landing,  accounts  of  early  settlements,  encounters 
with  the  Indian  tribes,  etc.,  should  not  be  omitted.  The  prin- 
cipal facts  concerning  the  settlement  of  the  several  States  of 
the  Union  may  be  presented  in  connection  with  their  geo- 
graphical description;  and  in  describing  cities,  mention  should 
be  made  of  the  principal  events  that  took  place  in  them,  and 
of  the  eminent  men  who  have  lived  there. 

Celebrated  buildings,  like  Girard  College  in  Philadelphi;i, 
lead  naturally  to  the  statement  of  facts  in  the  lives  of  their 
founders.  St.  Peter's  at  Rome  and  the  Vatican  could  not  be 
passed  over  without  telling  of  Michael  Angelo  and  Raphael. 
Westminster  Abbey  leads  one  to  tell  of  its  founder  and  the 
great  men  who  sleep  there ;  Faneuil  Hall  will  suggest  the 
deeds  of  Warren  and  Adams  ;  Inde[)endence  Hall  in  Philadel- 
phia will  remind  one  of  the  signers  of  the  Declaration  of 
Independence  and  the  Bell  of  Lil)ert3'.  The  same  method 
may  also  be  applied  to  natural  features.  The  Hudson  River 
will  remind  us  of  Hendrick  Hudson ;  Lake  Erie  of  the 
victory  of  Perry  ;  Boston  Harbor  of  the  great  tea-party  ; 
Lookout  Mountain  of  Gen.  Hooker  ;  Yicksburg  of  Gen.  Grant, 
etc.  Such  an  association  of  historic  events  with  places  will 
give  a  life  and  reality  to  the  places,  and  link  them  to  the 
memory  by  the  tie  of  interest. 

6.    The  course  of  instruction  in  primary  geography  should 
be  practical.     The  teacher  should   aim    to  make  the   subject 
life-like  and  real.     It  is  surprising  how  abstract  and  theoret- 
ical the  knowledge  of  geography  often  is  with  young  pupils 
Their  knowledge  of  the  map  is  often  merely  the  idea  of  so 


470  METHODS   OF   TEACHING. 

many  lines  and  black  spots  on  paper.  The  directions  of 
countries  from  each  other  are  often  all  confused  by  the  sec- 
tion map  the}'  studied,  and  the  position  of  the  seats  in  the 
school-room.  Ask  them  to  point  to  Europe,  and  they  will  as 
soon  point  north  or  west  as  east.  We  have  seen  children 
who  were  reciting  on  the  map  of  Brazil  point  north  for  South 
America. 

The  teacher  should  be  careful  also  to  present  tliose  facts 
which  are  the  most  im|)ortant  to  be  known.  There  is  no  .use 
in  remembering  all  the  little  rivers  of  Africa  or  the  smaller 
towns  of  Europe,  the  exact  areas  of  states,  and  the  population 
of  most  of  the  cities.  The  teacher  should  also  aim  to  connect 
the  facts  with  ever^'day  life.  Let  him  bring  in  a  newspaper 
and  read  of  events  occun-iug  in  different  places,  and  have  the 
pupils  to  locate  these  places.  Call  attention  to  railroads,  lines 
of  steamers,  etc. ;  and  show  them  how  we  should  travel  by 
land  or  water  from  one  place  to  another.  Show  also  how  one 
country  is  adapted  for  manufactures,  another  for  commerce, 
etc.  Endeavor  to  make  the  subject  a  reality  in  the  mind  of 
a  child,  and  not  a  mere  collection  of  words  or  abstract  marks 
on  a  map. 

7.  The  course  of  instruction  in  primary  geography  should 
be  given  orally.  For  primary  pupils  no  text-book  is  needed.. 
To  have  them  study  the  subject  in  a  text-book  at  first,  is  to 
have  them  commit  words  instead  of  learning  geograplij'.  The 
teacher  needs  a  globe  and  outline  majjs,  but  no  text-book  for 
the  first  year  or  two  in  teaching  primary  geography'.  The 
ideas  of  geography-  are  to  be  presented  by  real  objects,  or  hy 
models  or  pictures  of  them.  Localities  are  to  be  pointed  out 
on  the  map  and  globe,  and  the  descriptions  given  verbally  by 
the  teacher  and  remembered  and  repeated  bv  the  pupil.  After 
stating  a  fact,  the  pupil  should  repeat  it,  and  the  facts  given 
in  one  lesson  should  be  repeated  at  the  next  lesson.  Facts 
learned  in  this  wa}'  will  possess  an  interest  for  the  pupil  and 
maKe  a  permanent  impression  on  his  memor3^ 


TEACHING   GEOGRAPHY.  47] 

II.  Method  op  Teaching. — We  now  present  the  course  of 
instruction  in  Primary  Geograpli}'.  Tiie  lessons  should  be 
given  in  the  following  order:  1.  The  Perception  of  geograph- 
ical facts;  2.  Tiie  Conception  of  geographical  facts;  3.  The 
Representation  of  geographical  facts;  4.  The  Explanation 
of  geographical  facts. 

1.  Tlie  Perception  of  Oeofjraphical  Facts. — The  first 
step  in  teaching  geography  is  to  give  the  pupiis  geographical 
ideas  through  the  senses.  It  is  a  geographical  lesson  on  tliat 
which  the  pupils  can  observe  for  themselves.  It  employs  the 
objects  of  the  world  around  us,  or  models  or  pictures  of  them. 
This  stage  will  include  lessons  on  Land,  Water,  the  Soil,  the 
People,  Animals,  Plants,  and  Minerals. 

Nature  of  the  Lessons. — Lessons  on  Land  will  include  les- 
sons on  hills,  mountains,  plains,  islands,  capes,  isthmuses,  etc. 
Lessons  on  Water  will  include  springs,  ponds,  rivers,  lakes, 
ba3'S,  straits,  etc.  Lessons  on  Soil  will  include  the  different 
varieties  of  soil  found  in  the  neighborhood.  Lessons  on  the 
People  will  include  the  looks,  manners,  habits,  education,  re- 
ligion, etc.,  of  the  people  of  the  town  or  vicinity.  Lessons 
on  Animals  include  the  domestic  animals  and  the  principal 
wild  animals,  the  birds,  the  insects,  etc.,  found  in  the  vicinity. 
Lessons  on  Plants  include  the  trees  of  the  3'ard,  orchard,  and 
forest,  and  many  of  the  principal  plants  and  flowers.  Les- 
sons on  Minerals  include  quartz,  limestone,  sandstone,  and 
such  other  minerals  as  are  common  to  the  place,  or  of  which 
specimens  can  be  obtained. 

The  Method. — The  method  of  teaching  the  primary  ideas 
and  facts  of  geography  should  be  concrete  and  inductive. 
The  objects,  or  models  or  pictures  of  them,  should  be  pre- 
sented to  the  pupil,  if  possible.  We  should  also  pass  from 
the  ideas  to  the  terms  which  exjiress  them;  and  from  a 
clear  idea  of  the  meaningf  and  use  of  a  term  to  its  definition. 
Lessons  on  Land  and  Water. — The  pupils  should  be 
taken  out  of  doors  and  shov»-n  the  divisions  of  land,  and  be 


472  METHODS    OF    TEACHING. 

taught  their  names.  They  may  bo  shown  a  liill,  or  a  moun- 
tain, if  there  is  one  in  the  neighborhood.  They  should  be 
taken  down  to  the  river  that  they  may  see  an  island,  a  cape,  a 
peninsula,  an  isthmus,  etc.  The  teacher  should  also  show  the 
different  divisions  of  water  and  give  their  names.  Representa- 
tions with  the  "moulding  board"  or  the  "geographical  box," 
will  be  of  great  advantage  to  the  pupil.  Such  a  box  can  be 
easily  made,  with  depressions  and  elevations  carved  in  the 
wood,  and  water  poured  in  it,  to  represent  the  different  phys- 
ical features.  The  divisions  of  water  and  land  can  also  be 
represented  on  the  blackboard.  A  little  water  poured  upon 
the  school-room  floor  can  be  made  to  serve  the  same  purpose. 

Other  Lessons. — Pupils  should  be  shown  the  different 
varieties  of  soil,  as  sandy,  clayey,  etc.;  their  adaptation  to 
different  kinds  of  crops,  etc.  They  should  be  taught  to  ob- 
serve and  describe  the  peculiarities  of  the  people,  their  lan- 
guage, customs,  occupations,  interest  in  education,  religious 
beliefs  and  customs,  etc.  They  should  also  be  taught  the 
names  of  all  the  ordinary  trees  of  the  neighborhood,  and  to 
distinguish  them  by  their  leaves,  bark,  and  the  grain  of  the 
wood;  and  also  the  names,  habits,  and  peculiarities  of  the 
animals  of  the  neighborhood,  as  is  indicated  in  the  system  of 
object  lessons.  Such  a  drill  will  give  knowledge  which  will 
serve  as  the  basis  for  learning  about  such  things  distant  fiom 
home,  and  enable  the  instruction  to  pass  from  the  known  to 
the  unknown.  The  student-teacher  will  exemplify  this  stage 
in  a  model  lesson. 

2.  The  Conception  of  Geofjraphical  Facts.— The  Percep- 
tion of  geographical  facts  should  be  followed  by  the  Concep- 
tion of  those  which  cannot  be  perceived.  From  a  knowledge 
of  that  which  the  pupils  can  see,  they  should  be  led  to  a 
knowledge  of  similar  things  of  which  they  can  conceive.  The 
objects  of  perception  thus  become  the  basis  of  objects  of  con- 
ception. These  two  stages  may  to  a  large  extent  go  hand  in 
hand  in  actual  instruction. 


TEACHING    GEOGRAPHY.  473 

Nature  of  Lessons. — The  lessons  on  Land  include  moun- 
tains, plains,  prairies,  deserts,  table-lands,  volcanoes,  etc. 
Lessons  on  Water  include  rivers,  bays,  gulfs,  straits,  chan- 
nels, lakes,  oceans,  etc.  Lessons  on  People  may  include  the 
Indians,  Hindoos,  Chinese,  Japanese,  Esquimaux,  Africans, 
etc.  Lessons  on  Animals  include  lions,  tigers,  bears,  wolves, 
monkeys,  elephants,  alligators,  the  ostrich,  the  condor,  the 
eagle,  etc.  Lessons  on  Plants  include  the  tea-plant,  coflfee- 
plant,  cotton-plant,  bread-fruit,  banyan-tree,  cinnamon-tree, 
etc.  Lessons  on  Minerals  include  iron,  zinc,  copper,  lead, 
coal,  gold,  silver,  diamonds,  etc. 

Method  of  Teaching. — The  method  of  teaching  should,  so 
far  as  possible,  pass  from  the  perception  of  the  known  to  the 
conception  of  the  unknown.  Beginning  with  some  visible  ob- 
ject, the  mind  may  be  led  to  conceive  the  invisible.  The  facts 
of  sense  thus^  become  the  basis  of  the  ideas  of  conception ;  the 
thing  seen  becomes  the  representative  of  the  thing  to  be  con- 
ceived. By  means  of  the  imagination  we,  as  it  were,  trans- 
mute the  real  object  into  the  ideal  conception. 

Lessons  on  Land. — To  give  a  pupil  an  idea  of  a  Mountain, 
let  him  think  of  a  hill  which  he  has  seen,  and  imagine  it  to 
grow  higher  and  higher  until  it  is  half  a  mile,  a  mile,  two 
miles,  three  miles,  etc.,  high  ;  its  top  crowned  with  clouds 
and  on  its  summit  rfesting  perpetual  snow.  In  this  manner  a 
pupil  may  obtain  quite  a  definite  idea  of  a  mountain.  Then 
let  him  imagine  it  to  begin  to  stretch  out  further  and  further 
away  until  it  reaches  man}'  miles  bej^ond  the  horizon;  this 
will  give  an  idea  of  a  mountain  range. 

To  conceive  of  a  Prairie,  have  the  pupil  think  of  a  meadow 
and  then  imagine  it  to  begin  to  spread  out  in  every  direction^ 
furtlier  and  further  away,  until  it  reaches  many  milas  in 
extent ;  let  him  imaa^ine  the  srrass  growing  as  hisrh  as  his  head, 
adorned  with  a  profusion  of  rich  flowers,  and  inhabited  by 
prairie  birds,  herds  of  buffaloes,  and  droves  of  wild  horses. 
It  will  add  interest  to  the  conception  to  describe  a  prairie 


474  METHODS   OF   TEACHING. 

on  fire,  the  flames  traveling  with  great  speed,  and  buffaloes 
and  droves  of  wild  horses  fl^Mng  in  fright  before  them. 

A  Desert  can  be  conceived  by  beginning  with  a  small  level 
area  of  sand,  and  imagining  it  to  spread  out  in  every  direction 
until  it  covers  an  extent  of  many  mik-s — a  waste  of  parched 
sand,  dotted  here  and  there  with  bright  green  oases.  Tlii-y 
may  also  be  led  to  see  the  caravans  crossing  the  desert,  wi'  I 
the  camels  and  horses,  now  stopping  at  an  oasis,  and  no\ 
overtaken  by  a  storm  of  sand  from  which  the}'  can  escajH 
only  by  dismounting  and  covering  their  faces,  and  by  which 
they  are  often  buried  in  a  sandy  grave. 

Oth^r  Lessons. — In  a  similar  manner,  a  rivulet  ma}'  be  en- 
larged into  a  river,  a  pond  into  a  lake,  a  lake  into  an  ocean,  so 
wide  that  it  will  take  ships  weeks  to  sail  across  it.  Yivid 
conceptions  of  the  people  may  be  given  by  life-like  descrip- 
tions of  them,  as  the  Chinese  with  their  habits  so  opposite  to 
ours,  the  Hindoos,  with  their  dreamy  beliefs  and  cruel  relig- 
ious rites  ;  the  Indians,  with  their  wigwams,  bows  and  arrows, 
and  war  dances;  the  Esquimaux,  with  their  ice-huts,  dogs,  and' 
sledges.  Ideas  of  animals,  plants,  etc.,  can  also  be  given  ly 
descriptions  and  pictures  of  them. 

Adaptation. — These  facts  should  be  adapted  to  the  capacity 
and  taste  of  the  pupils.  The  teacher  will  readily  see  what 
things  are  interesting  to  the  young  learner,  and  will  be  able  to 
tell  how  far  to  enter  into  details  in  his  lessons.  Much  of  the 
interest  will  be  due  to  the  manner  of  the  description;  and  it  will 
aflbrd  the  teacher  an  excellent  opportunity  to  cultivate  an  easy 
and  artistic  method  of  describing  objects.  Let  it  be  remembered 
that  it  is  the  author's  opinion  that  no  teacher  is  competent  to  teach 
geography  until  he  is  able  to  give  such  descriptions.  The  student 
of  teaching  should  learn  how  to  give  the  lessons  suggested,  and 
extend  the  method  to  other  things  in  the  course. 

3.    Tlte    Represe^itation    of    Geof/rapJtical    Facts. — Thu 

next  step  in   geographical   instructi(jn   is   the  representation   of 
geographical  ideas  on  paper  in  the  form  of  a  map.     This  stage 


TEACHING   GEOGRAPHY.  475 

includes  both  the  Drawing  of  Maps  and  Lessons  on  Maps. 
It  beo-ins  with  srivius;  an  idea  of  direction,  then  showing  how 
to  indicate  direction,  then  the  making  of  a  map,  then  the 
study  of  outline  mops. 

Direction. — The  first  thing  is  to  teach  a  pupil  the  different 
directions.  We  may  do  this  by  having  him  stand  with  his 
face  to  the  north,  and  arms  extended,  the  right  hand  pointing 
to  the  east,  and  the  left  hand  to  the  west.  The  rising  and 
setting  sun  will  indicate  the  east  and  west ;  and  it  will  be  well 
to  have  the  pupil  fix  the  north  by  observing  the  position  of 
the  North  star  in  the  evening. 

Indicating  Directions — The  next  step  is  to  indicate  these 
directions.  Draw  a  north  and  south  line  on  the  floor,  and 
across  it  an  east  and  west  line;  and  call  attention  to  the  direc- 
tion of  objects  from  the  point  of  crossing.  Then  draw  these 
lines  on  a  horizontal  slate  or  piece  of  paper,  place  the  pupil  at 
the  south  end  of  the  slate  or  paper,  and  lead  him  to  see  that 
the  side  next  to  him  is  south;  the  side  from  him  is  north;  the 
rio-ht-hand  side,  east;  and  the  left-hand  side,  west. 

Relative  Directions. — These  are  now  a6.soZ«i!e  directions; 
the  next  step  is  to  lead  to  the  idea  of  relative  directions.  To 
do  this,  we  represent  on  slate  or  paper  some  of  the  objects  in 
the  school-room,  indicating  their  directions  from  one  another. 
We  then  gradually  change  the  position  of  the  slate  or  paper, 
still  calling  attention  to  the  fact  that  the  right  hand  indicates 
east,  the  left  hand  west,  the  upper  part  north,  etc.,  and  that 
the  objects  represented  have  the  same  relative  directions. 
Great  care  is  to  be  exercised  in  this  lesson,  that  the  pupil  may 
have  a  correct  idea  of  the  relative  directions  indicated  on  the 
map. 

MaJdng  a  Map The  next  step  is  to  make  a  map  nf  tin 

school-room,  locating  the  different  objects,  the  teacher  -;  .Il-I- 
the  platform,  the  stove,  etc.     Then  make  a  map  of  the  sdi-r. 
yard,  locating  the  objects  in  it.     Then  include  in  the  mai)  the 
neio-hborino-  fields  and  the  different  farms,  locating  the  roads. 


176  METHODS   OF   TEACHING. 

the  W(,  ods,  the  farm-houses,  the  barns,  etc.  Then  let  the  pupils 
draw  maps  of  their  own  homes,  their  gardens,  the  streets  of 
the  village,  indicating  the  principal  buildings,  etc.  They  may 
also  draw  imaginar}'  maps. 

Lesson  on  Maps. — We  should  next  pass  to  the  map  of  the 
township,  county,  or  state,  or  a  map  of  the  United  States  or 
the  world,  as  the  teacher  prefers.  The  pupil  should  then  have 
a  regular  drill  on  maps,  and  learn  what  is  called  Local  and 
Descriptive  Geography.  These  lessons  may  include:  1.  The 
pointing  out  and  naming  of  localities  ;  2.  The  description  of 
geographical  features ;  3.  Some  of  the  principal  historical 
events  relating  to  countries  and  places. 

Map  Draiviufj. — The  elements  of  Map  Drawing  may  now 
be  introduced.  The  first  lessons  should  be  entirely  by  imita- 
tion. No  method  of  triangulation  or  the  use  of  construction 
lines  should  be  used.  The  pupil  will  look  at  the  map,  and 
then  try  to  draw  the  map  from  memory.  At  first,  if  he  wishes, 
he  may  put  a  tliin  piece  of  paper  over  the  map  of  an  atlas  and 
trace  the  outline.  It  will  aid  in  giving  a  more  definite  idea 
of  the  contour,  and  will  serve  as  an  introduction  to  construct- 
ing a  map  from  memory.  Maps  should  be  drawn  on  the 
blackboard  as  well  as  on  paper. 

4.  The  Explanation  of  GeographUuil  Facts. — The  pupil  is 
now  prepared  for  the  Explanatory  Stage  of  Geography.  This 
includes  the  explanation  of  geographical  facts  and  |)henomena, 
especially  those  pertaining  to  the  astronomical  elements  of 
geography.  It  includes  the  Form  of  the  Earth,  the  Motions  of 
the  Earth,  the  lines  of  Latitude  and  Longitude,  the  Circles  on 
the  globe,  including  the  Equator,  the  Tropics,  the  Polar  Cir- 
cles, and  the  Zones. 

Form  of  the  Earth. — The  teacher  should  begin  hy  calling 
attention  to  the  apparent  form  of  the  earth.  Then  tell  them 
it  is  round  like  a  ball,  and  show  its  form  by  a  globe.  Give 
also  some  of  the  simple  proofs  of  its  rotundity,  as  the  appear- 
ance of  a  vessel  approaching  or  receding  from   the  shore,  the 


TEACHING  GEOGRAPHY.  477 

sailing  around  it,  etc.  A  magnetic  globe  will  illustrate  the 
first  proof.  We  then  show  that  the  surface  of  the  earth  con- 
sists of  land  and  water,  point  out  the  land  and  the  water,  name 
the  different  grand  divisions  of  land  and  water,  and  explain 
their  form,  position,  etc. 

TJie  Equator,  etc. — The  next  step  is  to  call  attention  to 
the  various  circles  of  the  globe  and  explain  their  uses.  The 
equator,  parallels,  and  meridians  should  be  introduced  by 
showing  their  use  in  locating  objects.  To  illustrate,  suppose 
we  mark  an  object  on  the  globe;  we  must  look  over  the  entire 
surface  to  find  it.  But  suppose  we  draw  a  line  around  the  mid- 
dle of  the  globe  and  saj'  the  object  is  above  or  below  this  line, 
then  j-ou  need  look  over  only  one-half  of  the  surface  to  find 
it.  Then  suppose  we  draw  lines  parallel  to  this  line,  which 
we  call  the  Equator^  and  say  the  object  is  on  one  of  these 
lines  ;  now  you  need  look  only  on  this  line  to  find  it.  Sup- 
pose now  we  draw  a  line  from  the  top  down  through  the  object ; 
we  can  locate  it  exactl}^  b}'  the  intersection  of  these  lines,  or 
by  saj'ing  it  is  so  many  units  above  the  equator  and  so  many 
units  to  the  right  or  left  of  a  given  line. 

We  then  give  their  names,  equator,  parallels,  and  vieridians, 
and  explain  the  division  of  the  circle  into  degrees,  etc.  We 
then  drill  in  finding  latitude  and  longitude  of  places,  and  in 
finding  places  b}"  the  latitude  and  longitude.  We  may  also 
show  them  that  the  extent  of  latitude  is  90°,  and  of  lonsfitude 
180°,  and  lead  them  to  see  what  places  have  no  latitude,  no 
longitude,  no  latitude  and  longitude.  In  this  way  pupils 
may  be  given  a  much  clearer  idea  of  the  nature  and  use  of 
parallels  and  meridians  as  locating  lines  than  they  usually 
possess. 

3Iotions  of  the  Earth. — The  next  step  is  to  teach  the  two 
motions  of  the  earth.  The  diurnal  motion  ma}'  be  illustrated 
by  the  revolution  of  a  globe  on  its  axis,  sliowing  the  phe- 
nomena of  day  and  night,  sunrise  and  sunset.  The  apparent 
motion  of  the  sun  may  be  illustrated  by  the  common  expert- 


478  METHODS   OF   TEACHING. 

ence  of  the  appare«t  motion  of  a  railroad  train  when  at  rest. 
The  annual  motion  and  its  effects  ma^*  be  illustrated  by  a 
tellurian,  cr  in  its  absence,  by  an  apple  or  a  pumpkin,  carried 
around  a  lamp  representing  the  sun.  The  common  globe  may 
also  be  carried  around  some  object  representin«  the  sun,  care 
being  taken  to  keep  the  axis  always  parallel  to  its  first  posi- 
tion, inclined  about  23^  degrees.  A  A'ery  clear  idea  of  the 
change  of  seasons,  etc.,  can  be  given  in  this  wa^'. 

Ajcitio/the  Earth. — The  next  step  is  to  call  attention  to 
the  axis  of  the  Earth,  as  the  centre  of  its  motion.  Explain 
that  this  is  inclined  to  the  orbit  about  23^°,  that  it  is  alwa\-s 
parallel  to  a  given  position,  and  that  the  ends  are  called 
Poles,  etc. 

Circles  auff  Zones. — The  next  step  is  to  explain  the  trop- 
ical and  polar  circles.  This  ma^'  be  done  by  the  tellurium,  or 
by  carrying  the  globe  around  a  lamp,  or  by  charts  or  diagrams 
on  the  board.  Let  them  see  that  in  one  part  of  the  orbit,  the 
sun  shines  23i°  over  one  pole  and  lacks  23i°  of  reaching  the 
other  pole,  which  will  fix  the  polar  circles.  Let  them  see 
that  in  one  jjosition  the  sun  is  exactly  over  a  point  23^° 
above  the  equator,  and  in  another  over  a  point  23^°  below  the 
equator,  which  will  fix  the  tropical  circles.  Then  explain  the 
meaning  of  a  zone  or  belt,  and  let  them  see  that  the  cold  or 
frigid  zones  ai-e  23|^°  wide ;  that  the  hot  or  torrid  zone  is 
23i°  +  23^°,  or  47°,  wide;  and  that  to  find  the  width  of  each 
temperate  zone,  we  add  the  width  of  the  frigid  and  the  torrid 
on  one  side  of  the  equator,  and  subtract  the  sura  from  90° ; 
thus,  23^°+23^°=47°;  90°— 4T°=43°. 

Lessons  on  Zones. — Lessons  Tuay  then  be  given  on  the 
productions  of  the  different  zones;  their  animals,  trees,  etc.; 
the  difference  in  the  inhabitants,  their  occupations,  etc. 
The  appearance  of  the  moon,  stars,  and  sun  in  circling  the 
heavens,  the  long  twilight,  the  long  nights  of  winter,  etc.,  ot 
the  frigid  zones,  will  be  interesting  to  the  pupils  ;  also  an  ac- 
count of  the  efforts  to  reach  the  North  Pole. 


TEACHING   GEOGRAPHY.  479 

liemarks. — Such  a  course  should  be  given  in  connection 
with  the  conceptive  and  representative  stages  of  the  subject. 
The  lessons,  as  indicated  in  these  stages,  may  be  continued 
several  months,  indeed,  in  a  graded  school  they  should  be 
continued  for  several  years,  before  the  pupil  takes  a  text-book 
to  study.  Tue  principal  part  of  the  course  will  be  the  local 
and  descriptive  elements  ;  the  maps  of  all  the  countries  should 
be  studied,  and  the  most  interesting  facts  stated  to  the 
puj)ils. 

If  the  pupils  have  a  book,  containing  a  few  of  the  more  in- 
teresting facts,  to  read  (not  to  commit  for  recitation),  it  will 
add  interest  to  the  lesson,  and  give  them  something  to  look 
at  outside  of  the  recitation.  The  teacher  should  make  out  an 
outline  of  a  little  lext-book  on  geograph;/,  and  follow  this 
course  in  his  instruction.  It  will  add  greatly  to  the  teacher's 
knowledge  and  to  the  interest  of  liis  jnipils.  Indeed,  a 
teacher  who  is  not  able  to  carry  out  sucli  a  course  in  geog 
raph}',  is  so  far  not  thorouglily  pi('i)arecl  to  teach  the  subject, 

11.  Teachtxg  Advanced  Geography. 

The  Advanced  Course  in  Geography  embraces  a  full  school 
course  in  local  and  descriptive  geography.  It  includes  the 
formal  study  and  recitation  of  the  subject.  The  pupils  are 
expected  to  study  the  lesson  in  a  text-book,  and  come  to  the 
recitation  prepared  to  recite  what  they  have  learned.  We 
shall  speak  briefly  of  the  Principles  of  Instruction  in  this 
course,  and  of  the  Methods  of  Teaching  the  course. 

I.  Principles  of  Teaching. — There  are  several  principles 
b}"  which  the  teacher  in  the  advanced  course  in  geograph}' 
should  be  guided.  The  three  most  important  are  the  fol- 
lowing: 

1.  The  course  in  advanced  geography  should  be  analytic 
rather  than  synthetic.  We  should  begin  at  the  world  as  a 
whole,  and  stud\'  from  the  whole  to  its  parts,  or  we  should 


480  METHODS   OF   TEACHING. 

begin  with  a  larger  division  and  come  down  gradually  to  the 
smaller  divisions  of  countries.  The  course  should  proceed 
from  the  general  to  the  particular;  from  the  whole  to  its 
parts. 

2.  The  course  in  advanced  geography  should  extend  to  the 
classification  of  geographical  facts.  The  child  begins  geog 
r;i[»liy  with  details,  but  it  will  be  of  advantage  to  group  these 
tU'tails  into  classes  or  systems  of  facts.  Thus,  after  a  knowl- 
etlue  of  several  of  the  particular  rivers  of  a  country,  we  may 
classify  them  into  river  S3'stcms,  and  study  them  as  such. 
So  from  a  knowledge  of  individual  mountains  we  ma^^  pass  to 
their  chissification  into  sj'stems,  and  study  the  mountain 
systems  of  the  globe.  The  method  to  be  pursued  is  thus  in- 
ductive rather  than  deductive. 

3.  The  course  in  advanced  geography  may  also  include  an 
inquiry  into  the  causes  of  geographical  phenomena.  The  facts 
of  geography  will  include  some  of  the  striking  facts  and  phe- 
nomena of  the  globe,  a-nd  the  child  will  naturall3^  inquire  after 
the  causes  of  them;  and  it  will  be  well  to  gratify  this  inquiring 
spirit.  We  ma}'  explain  the  causes  of  volcanoes,  earthquakes, 
hot  springs,  ocean  currents,  etc.  We  may  call  attention 
to  the  circumstances  which  determine  the  location  of  cities, 
the  causes  of  the  prosperity'  of  nations,  the  reason  for  certain 
industries,  etc.  Such  instruction  may  be  mingled  with  the 
facts  of  the  course,  or  it  may  be  presented  at  the  close  of  the 
book,  or  in  the  form  of  a  general  review  of  the  subject. 

II.  Methods  of  Teaching. — The  course  in  advanced  geogra- 
phy should  include  the  following  subjects :  1.  Definitions ; 
2.  Description ;  3.  Lesson  on  Maps  ;  4.  Drawing  Maps ;  5. 
Interesting  Facts;  6.  Imaginary  Travels;  7.  Geographical 
Outlines;  8.  Classification  and  Causes  of  Geographical  Facts. 

1.  liefiultiotxs. — Pupils  should  be  required  to  give  defini- 
tions of  the  principal  terms  used  in  geography.  Thus,  they 
should  be  required  to  define  a  river,  a  lake^  an  ocean,  a  hill,  a 
mountain,  an  island,  etc.      In   these  definitions  we  cannot 


TEACHING    GEOGRAPHY.  481 

always  pretend  to  scientific  accuracy,  but  it  is  thought  to  be 
of  advantage  to  the  student  to  give  statements  approximating 
such  definitions  as  closely  as  possible.  Tlie  ideas  of  these 
geographical  objects  were  obtained  in  the  elementary  course ; 
the  pupil  should  now  be  required  to  express  these  ideas  in  the 
form  of  definitions. 

2.  Descriptions. — The  pupils  should  also  be  required  to 
learn  the  descriptions  as  given  in  the  text-book,  and  to  present 
the  same  in  the  recitation.  They  should  not  commit  the  text 
verbatim,  but  be  encouraged  to  give  the  matter  partly  in  their 
own  language.  The  recitations  should  be  largelj'  topical, 
though  points  omitted  ma^'  be  brought  out  by  questions.  The 
descriptions  may  be  given  in  connection  with  the  map  or  with- 
out it.  The  pupil  should  learn  to  describe  away  from  the 
map  as  well  as  on  it;  for  in  his  reading  he  will  not  have  the 
map  before  him,  and  he  must  learn  to  conceive  geographical 
localities  without  the  map.  The  pupils  may  be  encouraged  to 
give  any  facts  bearing  upon  the  subjects  considered,  not  found 
in  the  text-book  used  in  the  school.  , 

8.  Lessons  on  Maps. — In  connection  with  the  descriptions 
there  should  be  constant  lessons  on  maps.  Pupils  should  be 
thoroughly  drillerl  in  local  geography,  for  they  need  to  know 
the  location  of  places.  For  this  purpose  pupils  should  have 
atlases,  and  there  should  be  outline  maps  in  the  school. 
These  lessons  on  maps  ma}^  be  given  in  several  different  ways. 
First,  the  pupil  may  stand  at  the  outline  map,  and  with  a 
pointer  point  out  and  name  localities.  Second,  one  pupil  may 
point  out  and  another  pupil  may  name  the  places  indicated. 
Third,  one  pupil  may  stand  at  his  seat  and  name  certain 
places,  and  another  pupil  standing  at  the  map,  may  point  them 
out.  Fourth,  the  teacher  may  point  out  and  the  pupils  name, 
or  the  teacher  name  and  the  pupils  point  out  places.  Care  is 
to  be  taken  that  the  map  is  made  a  means  to  and  not  the  end 
of  geographical  knowledge;  a  knowledge  of  the  position  of 
so  many  lines  and  spots  is  worthless,  unless  they  are  sug- 
gestive of  the  realities  of  nature. 

21  • 


482  METHODS   OF   TEACHING. 

4.  Dratring  JIaps. — The  pupils  should  be  required  to  draw 
maps  as  well  as  to  study  them.  There  are  several  reasons  for 
map-drawing  in  the  study  of  geography.  First,  it  aids  the 
pupil  to  fix  the  physical  features  in  the  memory,  by  requiring 
a  closer  and  more  minute  observation  than  is  necessary  for 
mere  description.  Second,  it  begets  a  habit  of  close  and  ac- 
curate observation  in  the  study  of  raajis.  Third,  it  gives  skill 
in  representation,  which  may  be  of  advantage  to  the  pupil  in 
many  circumstances  in  life. 

Methods. — There  are  two  methods  of  map-drawing  ;  that  of 
simple  imitation  and  that  of  construction  lines.  By  the 
former  method,  the  pupil  looks  closely  at  the  map,  and  then 
endeavors  to  reproduce  it' by  merely  imitating  the  model. 
By  the  other  method,  certain  lines  are  drawn  to  guide  the 
pupil  in  obtaining  the  correct  form  and  outline.  With  young 
puj)ils  we  should  depend  mainly  on  imitation;  with  older 
pupils  construction  lines  may  be  used  Avith  advantage.  The 
system  of  construction  should,  however,  be  simple;  the  com- 
plicated systems  of  some  authors  are  a  waste  of  time. 

5.  Interrstinff  Facts. — The  teacher  should  add  to  the  text 
interesting  geographical  and  historical  fiicts.  In  no  subject 
taught  in  the  common  schools  is  there  such  a  fine  opportunity 
for  the  teacher  to  use  his  general  knowledge,  and  awaken  an 
interest  in  the  study  by  additions  to  the  text-book.  The 
knowledge  gained  by  travel  or  reading  descriptions  of  foreign 
countries,  can  all  be  made  available  in  the  gcographv  class. 
The  study  of  good  works  on  travel  will  be  of  great  advantage 
to  the  geography  teacher;  and  we  recommend  him  to  read 
such  works  extensive!}'.  Photographs  of  celebrated  places, 
cities,  buildings,  natural  scenerj',  etc.,  will  add  greatly  to  the 
interest  of  pupils.  There  should  be  a  stereoscope  and  a  col- 
lection of  views  in  every  public  school. 

6.  liiKKjiiKirij  Travels. — Much  interest  can  be  awakened 
by  means  of  imaginary  travels  and  vo^'ages.  Thesp  ™f-3'  be 
given  in  several  different  wj^s.     First,  the  teacher  may  inquire 


TEACHING   GEOGRAPHY.  483 

how  we  nia}'^  travel  from  one  place  to  another,  as  from  New 
Vork  to  Chicago ;  and  have  the  pupils  point  out  and  describe 
the  trip.  Second,  the  teacher  can  describe  a  trip  or  voyage, 
giving  a  description  of  the  places  at  which  he  stops,  not  their 
names,  and  have  the  pupils  name  the  places  from  the  descrip- 
tion. Third,  the  pupils  may  be  required  to  prepare  descrip- 
tions of  imaginary  travels  and  voyages,  the  class  naming  the 
places  as  they  are  described. 

1.  Geographical  Outlines. — The  pupils  are  now  ready  to 
classify  their  knowledge  of  geography,  and  they  should  be  re- 
quired to  commit  and  use  an  outline  in  describing  the  different 
countries.  Such  an  outline  will  be  valuable  in  aiding  them  to 
collect  and  remember  geographical  facts.  With  such  an  out- 
line, they  can  acquire  the  knowledge  from  different  books,  if 
it  is  desired ;  all  that  is  needed  is  that  the  facts  they  know  be 
grouped  according  to  the  same  method. 

The  following  is  a  simple  and  convenient  outline.  It  may 
be  used  in  connection  with  any  country  or  state,  by  making 
such  slight  modifications  a«  the  subject  naturally  suggests. 

!1.  Position.  rl.  Appea'-ance. 

2.  Extent.  4.  The  People  \  2.  Customs. 

3.  Contour,  (.3.  Pursuits,  etc. 

(1.  Land.  ( 1 .  Cities  and  Towns. 

2.  Water.       5.  Their  Works  \  2.  Public  Works. 
•S.  Climate.  i  3.  Buildings,  etc. 

rl.  Animal. 
.  NaturaH  2.  Vearetable.  fl. Government. 


3.  Products. 


(  3.  Mineral.      6.  Institutions  \  2.  Education, 
r  1.  Animal. 
2.  Artificial  \  2.  Vegetable. 


rl.  Animal.  (. 3. Religion. 

;  \  2.  Vegetable. 
[  3.  Manufactures. 


•/ 


IV,  Teaching  Physical  Geography. 

Definition. — Physical  Geography,  in  its  literal  sense,  treats 
of  the  physical  features  of  the  earth,  that  is,  of  the  earth  as 
unmodified  by  man.  In  this  country,  however,  the  term  has 
acquired   a  special  signification,  meaning  the  philosophy  of 


484 


METHODS  OP  TEACHINQ, 


geography.     In  this  sense,  it  treats  of  the  classification   of 
geographical  facts  into  systems,  and  presents  the  laws  and  , 
causes  of  these  facts. 

Methods  of  Teaching — Little  need  be  said  concerning 
methods  of  teaching  the  subject.  The  pupil  will  study  it  from 
a  text-book  and  recite  it.  The  general  recitation  should  be 
topical ;  but  the  teacher  should  see  by  questions  that  the  pupil 
understands  the  subject.  Illustrations  on  the  blackboard 
should  be  constantly  required,  and  some  cliarts  and  apparatus 
will  occasionally  be  of  service.  The  best  books  we  have  ex- 
amined upon  the  subject  are  Warren's,  Mitchell's,  and  Hous- 
ton's; but  Guyot's  Earth  and  Man  should  be  in  every  teach- 
er's library. 

Divisions. — The  subject  may  be  treated  under  the  divisions 
indicated  by  the  following  Outline: 


I.  Earth  as  a  Planet. 

1.  Form  and  Size. 

2.  Motions  and  Orbit. 

3.  Circles  and  Zones. 

4.  Times  and  Seasons. 
II.  The  Land. 

1.  Inside  of  Earth. 

1.  Internal  Heat. 

2.  Volcanoes. 

3.  Earthquakes. 

2.  Outside  of  Earth. 

1.  The  Structure. 

2.  Distribution  of  Land, 

3.  General  Forms. 
♦             4.  Special  Forms. 

V.  Organic  Life. 

1.  Botany. 

2.  Zoology. 

3.  Ethnography. 


III.  The  Water. 

1.  Continental  Waters. 

1.  Springs. 

2.  Rivers. 

3.  Lakes. 

2.  Oceanic  Waters. 

1.  The  Ocean. 

2.  Ocean  Movements. 

3.  Ocean  Currents. 
rV.  The  Atmosphere. 

1.  Properties. 

2.  Temperature. 

3.  Moisture. 

4.  Winds. 

5.  Climate. 

6.  Storms. 

7.  Electric  and 
Optical  Phenomena. 


HISTORY. 


CHAPTER  I. 

TEACHING   HISTORY. 


HISTORY  is  a  narration  of  the  events  which  have  occurred 
among  mankind.  It  describes  the  past  actions  of  man- 
kind, the  rise  and  fall  of  nations,  and  the  changes  in  the  polit- 
ical and  social  condition  of  the  human  race.  In  its  higher 
departments,  it  seeks  also  for  the  causes  which  have  been 
operative  in  producing  these  events.  The  term  is  derived 
from  the  Latin  historia,  which  is  from  a  Greek  word  of  nearly 
the  same  form,  meaning  to  learn  or  know  from  inquiry.  The 
word  was  first  used  by  Herodotus  near  the  beginning  of  his 
work;  and  it  is  supposed  that  he  thus  fixed  the  sense  in 
which  it  has  since  been  used. 

Divisions. — History  is  divided  into  two  great  branches  ; 
the  Facts  of  History,  and  the  Philosophy  of  History.  The 
Facts  of  History  embrace  the  orderly  and  systematic  state- 
ment of  the  events  that  have  occurred  in  the  lives  of  indi- 
viduals and  nations.  The  Philosophy  of  History  endeavors 
to  ascertain  the  causes  which  have  contributed  to  produce  the 
different  changes  in  society  and  nations,  and  from  these  to 
predict  the  future  condition  and  destiny  of  mankind. 

History  is  also  divided  into  Ancient,  Mediseval,  and  Modern 
History.  Ancient  History  is  considered  as  ending  about  4Y6 
A.  P.,  the  date  of  the  destruction  of  the  western  division  of 
the  Roman  empire ;  Medifeval  History,  or  the  history  of  the 
Middle  Ages,  extends  from  476  A.  P.,  to  very  near  the  dis- 
covery of  America  by  Columbus  ;  Modern  History  begins  at 

(485) 


486  METHODS   OF   TEACHING. 

or  near  the  discovery  of  America,  and  extends  down  to  the 
present  time.  History  is  also  divided  into  Sacred  and  Pro- 
fane; and  still  other  divisions  are  sometimes  made. 

The  Facts. — The  Facts  of  History  differ  in  some  respects 
from  the  facts  of  the  other  sciences.  They  are  facts  that 
have  occurred  in  the  past  and  are  not,  therefore,  subject  to 
present  observation.  They  are  thus  known  only  tlirough  tes- 
timony, either  oral  or  written,  and  must  be  accepted  on  au- 
thority. They  are  also  connected  by  the  relation  of  time, 
rather  than  by  that  of  kind  and  quality,  like  the  facts  of  the 
other  sciences.  They  are  the  acts  of  free  agents,  proceeding 
from  the  operation  of  a  spiritual  being  not  governed  by  inex- 
ora1)le  law,  like  the  forces  of  nature,  but  which  is  a  law  unto 
itself,  and  which  freely  chooses  its  course  among  the  external 
circumstances  that  are  the  conditions  of  its  actions. 

The  Philosophy. — History  was  formerly  only  a  recital  of 
the  actions  of  mankind  ;  but  recently  attempts  have  been 
made  to  form  a  Philosophy  of  History.  The  great  thinkers 
of  the  world  have  looked  over  the  drama  of  human  experi- 
ence, and  have  endeavored  to  ascertain  the  influences  which 
have  been  operative  in  moulding  the  events  of  the  world. 
The  object  has  been  to  trace  the  action  of  causes  and  deduce 
certain  principles  which  may  serve  as  a  guide  to  statesmen 
and  rulers  in  conducting  the  affairs  of  nations.  Viewed  in 
this  light,  history  has  been  happily  styled  "  philosophy  teach- 
ing by  example." 

Systems. — Among  these,  three  great  classes  of  thinkers 
have  presented  three  distinct  methods  of  explaining  the  exist- 
ence of  historic  events.  These  three  theories  are  denomi- 
nated the  Materialistic,  the  Spiritualistic,  and  the  Theistic 
theories  The  Materialistic  Theory  holds  that  the  events  of 
histor^^  are  caused  by  the  physical  conditions  by  whic  h  man 
has  been  surrounded.  The  Spiritualistic  Theory  holds  that 
man  is  a  free  agent  and  has  determined  his  own  actions  in 
view  of  the  circumstances  under  which  he  was  placed.     The 


TEACHTXG    HISTORY.  487 

Theistic  Theoiy  maiatains  that  man's  actions  have  been  deter- 
mined, by  conditions  imposed  upon  him  by  God. 

Difjiculties. — History  presents  many  difficulties  not  met 
with  in  the  other  branches  of  knowledge.  Many  of  the  events 
occurred  so  far  back  in  the  past  that  it  is  impossible  to  know, 
in  many  cases,  whether  what  is  recorded  is  true.  Many  of 
them  have  been  handed  down  b}'  tradition,  and  are,  no  doubt, 
partially  if  not  wholly  false.  The  prejudices  of  mankind 
have  so  warped  their  judgment  and  statement  of  the  events 
of  tiieir  times  that  it  is  difficult,  if  not  impossible,  to  know 
what  was  the  truth  in  particular  cases.  Several  long-believed 
historical  statements  have  recentU'  been  shown  to  be  untrue; 
and  we  know  not  how  many  things  we  believe  to  be  facts  that 
never  occurred.  So  great  are  these  difficulties  that  Walpole 
declai'es  "all  history  to  be  a  lie;"  Napoleon  said,  "  History  is 
but  a  fable  agreed  upon;"  and  Dumas  remarks  that  "Truth  is 
very  liable  to  be  left-handed  in  history." 

In  the  philosoph}'  of  history,  the  difficulties  are  still 
greater.  The  motives  of  different  men  are  so  different,  the 
effects  of  circumstances  on  different  persons  are  so  diverse, 
the  influences  of  the  external  world  on  people  var}'  so  greatly 
with  their  intellectual  development  and  the  moral  influences 
thrown  around  them,  that  the  attempt  to  ascertain  the  causes 
of  men's  actions,  and  to  predict  the  future  condition  of  the 
race,  is  a  problem  of  surpassing  difficulty. 

Hisforicul  irorks. — The  works  on  tlie  facts  of  histor}'^ 
may  be  classified  into  tiie  Fragments  of  History,  Universal 
Histor}',  Compends  of  History-,  and  Detailed  History.  Frag- 
ments of  History  embrace  the  events  of  a  particular  period 
or  the  life  of  some  particular  person.  Universal  History  pre- 
sents an  account  of  the  principal  nations  of  the  globe  in  a 
connected  narrative.  Compends  of  History'  embrace  a  brief 
and  comprehensive  narration  of  tlie  events  of  a  nation  or  of 
several  nations.  Detailed  History  contains  a  full  account 
of  some  nation,  people,  or  particular  person  or  event. 


488  METHODS   OF   TEACHINQ. 

Value  of  Hisfori/. — The  teacher  should  have  a  clear  idea 
of  the  relation  of  a  subject  of  study  to  a  general  system  of 
education.  He  should  know  its  object  and  importance,  that 
he  may  be  able  to  teach  it  with  appreciation  and  skill.  A  few 
words  will  therefore  be  said  concerning  the  value  of  the  study 
of  history. 

1.  Hie  study  of  history  gives  culture  to  the  memory. 
Historj'  consists  of  a  narration  of  facts.  These  facts  are  to 
be  committed  to  memory;  they  are  valuable  to  the  student 
only  as  the}'  are  retained  in  the  mind.  They  cannot  be 
thought  out,  they  can  only  be  acquired  and  remembered  ;  hence 
history  is  especially  a  memory  study.  Only  a  person  with  a 
good  memory  can  become  well  versed  in  history;  and  among 
all  the  studies  history'  stands  lirst  in  giving  exercise  and  cul- 
ture to  the  memory. 

2.  History  gives  culture  to  the  imagination.  It  deals  with 
events  and  incidents,  and  these  lise  up  before  the  mind  as 
pictures  of  human  action.  To  study  history  properly,  the 
student  must  imagine  the  scenes  as  they  are  poitrayg^  by 
the  pen  of  the  historian.  The  events  of  the  past  should  pass 
before  the  mind  like  the  pictures  of  a  panorama.  This  brings 
the  imagination  into  vigorous  activity  and  affords  it  a  fine 
field  for  its  operations.  Indeed,  no  school  study  affords  such 
an  opportunity  for  the  culture  of  the  imagination  as  history. 

3.  History  cultivates  the  power  of  probable  reasoning.  Not 
only  are  the  facts  of  history  to  be  remembered,  but  their 
causes  are  to  be  ascertained  and  the  probable  effects  esti- 
mated. This  requires  what  is  called  probable  reasoning. 
The  historian  must  weigh  consequences,  estimate  the  effect 
of  conflicting  and  interacting  causes,  and  with  a  sure  pre- 
vision endeavor  to  read  the  future  result.  Historj''  thus 
trains  that  power  which  prep!ires  for  thinking  correctly  on 
the  practical  affairs  of  life,  to  a  greater  extent  than  any 
other  subject,  unless  it  be  Ethics  or  Political  Econom3\ 

4.  The  study  of  history  gives  moral  culture.    History  deals 


TEACHING   HISTORY.  489 

with  the  actions  of  mankind;  and  these  actions  contain  a 
moral  element.  We  see  the  motives  which  inspire  and  the 
results  which  flow  from  these  actions.  We  see  the  conse- 
crated labors  of  the  good,  the  devotion  of  the  patriot,  the 
fortitude  of  the  martyr,  and  our  souls  in  admiration  are  lifted 
up  into  a  higher  plane  of  moral  feeling.  We  see  the  mean- 
ness of  the  ignoble,  the  craft  and  falsehood  of  the  unprinci- 
pled, the  corruptions  of  the  base  and  degraded;  and  the  soul 
turns  instinctively  away  from  the  low  and  vicious  to  the  pure 
and  virtuous.  The  noble  and  the  ignoble,  the  generous  and 
the  selfish,  as  they  stand  contrasted  in  the  pages  of  historj-, 
awaken  in  us  admiration  for  the  right,  and  detestation  for  the 
evil.  We  long  to  emulate  the  deeds  of  heroes  and  patriots, 
and  thus  a  desire  for  good  and  noble  actions  is  excited  in  the 
mind.  For  moral  culture,  a  boy  should  go  to  history  rather 
than  to  moral  philosophy. 

5.  The  study  of  history  prepares  for  citizenship.  In  it  we 
read  of  the  value  of  wise  and  wholesome  laws,  and  of  the  politi- 
cal vices  that  sap  the  foundations  of  society  and  the  state; 
and  thus  learn  what  to  do  and  what  to  avoid  to  secure  the 
good  and  the  honor  of  one's  countrv.  This  knowledire  is 
especially  useful  in  a  republic,  where  every  man  is  u  voter. 
The  freeman's  ballot  should  be  an  intelligent  ballot ;  an  igno- 
rant ballot  is  a  curse  to  a  republic.  Every  vot?r  should  be 
familiar  with  the  past  history  of  his  country,  and  should  be 
guided  in  his  voting  by  lessons  of  wisdom  learned  from  the 
actions  of  the  wise  men  who  have  shaped  the  destinies  of  the 
nation.  The  flame  of  patriotism  is  kindled  and  nourished  by 
the  stud}'  of  the  patriotic  deeds  of  our  forefathers  ;  and  the 
object  of  school  studies  is  to  make  patriotic  citizens  as  well 
as  wise  and  virtuous  men. 

jyii'istonsfor  Teaching. — For  the  purpose  of  instruction 
we  divide  the  subject  of  history  into  three  parts  :  1.  The  Ele- 
ments of  Histor3' ;  2.  The  Advanced  Course  in  Historj-;  H 

The  Philosophy  of  History.     We  shall  give  a  brief  discussion 
21* 


490  METHODS    OF   TEACHING. 

of  the  methods  of  teaching  the  Elements  of  History  and  the 
Advanced  Course  in  History  ;  but  the  Philosophy  of  His- 
tory, not  being  appropriate  to  the  public  school,  will  not  be 
considered. 

I.  Teaching  the  Elements  of  History. 

B}'  the  Elements  of  History  we  mean  such  elementary 
instruction  as  every  j'oung  pupil  is  prepared  to  receive  before 
it  is  thought  best  to  have  him  stud}'  and  recite  the  subject 
from  a  text-book.  It  embraces  a  large  number  of  interesting 
events  and  incidents  which  are  suited  to  the  taste  and  capa- 
city of  young  pupils.  We  shall  mention  a  few  Principles  of 
Instruction  to  guide  the  teacher  in  his  work,  and  then  briefly 
indicate  the  Method  of  Instruction. 

I.  Principles  of  Instruction. — The  teacher  of  the  Elements 
of  History  should  be  guided  b}'  the  following  principles.  The 
necessity  of  these  principles  is  enhanced  by  the  fact  that  the}' 
have  been  frequently  violated  ;  and  that  the  vicious  methods 
used  have  generated  a  distaste  for  the  study  in  the  minds  of 
learners. 

1.  Instruction  in  the  elements  of  history  should  he  given 
orally.  No  text-book  should  be  used  in  the  early  lessons  in 
history.  The  pupil  is  not  to  be  required  nor  permitted  to 
prepare  and  recite  a  lesson  from  a  text-book.  The  child  who 
attempts  to  learn  history  from  a  text-book  usually  commits 
the  words  but  learns  little  history  ;  the  histor'ii,!  fact  escapes 
his  attention  in  his  effort  to  commit  and  recitt  the  words  of 
the  book.  The  teacher  is  to  give  the  facts  orally,  and  have 
the  pupil  remember  and  reproduce  them.  There  is  no  objec- 
tion to  the  pupils  reading  a  book  on  the  subject;  but  the  com- 
mon method  of  having  young  pupils  recite  lessons  from  a  text 
book  should  be  discontinued. 

2.  Instruction  in  the  elements  of  history  should  begin  at 
home  We  should  first  give  the  pupil  some  knowledge  of  the 
history  of  his  own  countrv.    He  will  be  more  inteiested  in  tlie 


TEACHING    HISTORY.  491 

events  occurring  in  his  own  land,  and  will  understand  them 
better.  From  the  events  occurring  here,  he  will  naturally  de- 
sire to  pass  to  the  events  which  transpired  in  other  countrieo. 
Thus,  from  the  history  of  America  we  are  naturally  b.d  to  the 
history  of  England  and  France;  from  these  we  pass  naturally 
to  Rome  and  Greece,  which  in  their  turn  lead  us  to  Syria,  Per- 
sia, and  Judea.  It  is  thus  clear  that  we  should  begin  at  home, 
pass  to  the  history  of  related  countries,  and  then  from  the  his- 
tory of  i)articular  countries  to  General  History. 

3.  The  basis  of  instruction  in  the  elements  of  histortj  is 
biographi/.  Children  are  more  interested- in  persons  than  In 
events.  What  a  man  did ;  how  he  struggled  and  suffered  and 
triumphed  ;  what  he  accomplished  or  how  he  failed  ; — all  this 
is  of  absorbing  interest  to  a  child.  Primary  history  should, 
therefore,  be  largely  personal.  Biography  is  the  soil  out  of 
which  the  tree  of  history  is  to  grow  for  a  beginner.  The 
events  of  history  are  to  be  made  to  cluster  around  some  per- 
sonal character;  the  life  of  some  great  leader  or  i)atriot  is  to 
be  the  centre  from  which  we  are  to  view  the  historic  story. 

4.  The  first  lessons  in  history  should  be  presented  in  the 
form  of  narratives.  Children  are  fond  of  story-telling. 
They  will  listen  for  hours  absorbed  in  the  relation  of  inter- 
esting personal  events.  It  was  thus  that  the  traditions  of 
nations  were  sung  or  rehearsed  in  the  early  days  of  the 
woild.  Our  fathers  refer  with  delight  to  the  revolutionary 
stories  which  were  told  to  them,  when  children,  by  their 
sires  or  grandsires,  around  the  fire  of  a  winter  evening. 
Such  incidents  linger  in  the  memory,  and  cultivate  a  taste 
for  historic  knowledge,  which  in  the  present  generation  seems 
to  be  on  the  wane.  Let  the  teacher  fill  his  mind  with  the 
stories  of  history,  and  relate  them  to  his  pupils,  and  he  will 
find  breathless  attention  and  a  growing  interest  in  historic 
knowledge. 

5.  Instruction  in  the  elements  of  history  should  be  given  in 
connection    with    geography.      History   and    geography   are 


492  METHODS   OF   TEACHING. 

closely  related,  both  in  their  nature  ant?  interest.  To  know 
the  location  of  a  country  and  the  character  of  its  people,  is 
to  awaken  the  inquiry,  Wlien  was  it  settled?  by  whom?  and 
what  has  contributed  to  its  growth  and  development?  His- 
tory and  geography  should,  therefore,  go  hand  in  hand  in 
primary  instruction.  We  should  give  historic  facts  in  con- 
nection with  our  lessons  in  geography,  linking  the  historic 
events  to  the  localities  of  the  maps  which  we  name  .".ud 
describe. 

II.  Methods  of  Teacuino. — These  general  principles  indi- 
cate the  character  of  the  course  in  teaching  histor3'  to  begin- 
ners. We  present  also  a  brief  statement  of  the  method  to  be 
em])loyed  in  actual  instruction.  • 

Teacher\s  Statement. — The  teacher  will  state  but  a  few 
facts  at  a  time,  and  then  have  the  pupils  repeat  these  facts. 
He  will  then  state  a  few  more  facts,  and  have  them  repeated. 
Then  have  both  groups  of  facts  repeated;  and  then  proceed 
to  a  new  statement.  It  is  a  mistake  to  repeat  too  many  facts 
at  one  time,  as  the  pu})ils'  minds  will  begin  to  wander, 
and  very  little  will  be  understood  or  retained.  When  the 
lesson  is  a  connected  narrative,  the  unbroken  statement  may 
be  longer,  as  the  interest  of  the  story  will  hold  the  pupils'  at- 
tention. 

Teacher's  Manner. — The  teacher's  manner  should  be  con- 
versational. He  should  be  careful  to  avoid  a  mechanical  n^nd 
declamatory  method  of  speaking.  Do  not  attempt  to  give 
lectures  on  history  to  little  children.  We  have  seen  teachers 
take  all  the  interest  out  of  the  subject  by  the  neglect  of  this 
simple  suggestion.  There  should  be  a  plain  narration  of  facts, 
in  a  simple  conversational  style,  as  if  the  teacher  were  talking 
familiarly  with  the  pupil.  He  should  also  endeavor  to  portray 
the  events  so  that  they  will  stand  out  as  pictures  before  the 
child's  mind,  and  seem  not  like  a  school-room  task,  but  like  a 
reality,  to  them. 

Pupil's  Recitation. — The    pupil's    statement    should    be 


TEACHIXG    HISTORY.  498 

partly  topical  and  partly  interrogative.  Call  on  one  to  tell 
all  he  can,  and  then  on  another  to  add  what  may  be  omitted, 
and  then  on  another,  etc.  Let  one  tell  one  thing,  and  another 
another  thing,  when  the  lesson  can  l)e  naturally  divided  into 
parts.  It  is  interesting  to  see  how  the  eyes  will  flash  as  a 
new  fact  rises  into  the  memory  which  was  forgotten  by  the 
pupil  reciting.  When  there  are  iiicts  not  remembered,  let  the 
teacher  call  them  out  by  appropriate  questions.  Then,  after 
all  the  facts  are  brought  before  the  mind  again,  let  some  one 
give  the  whole  story,  connecting  all  the  events  together  in 
their  proper  order.  Do  not  be  afraid,  with  little  children,  to 
have  them  tell  the  story  over  and  over,  as  their  interest  in 
the  relation  will  prevent  their  tiring  of  the  facts  related. 

Biography. — The  teacher  should  remember  to  make  l)iog- 
raphy,  so  far  as  possible,  the  basis  of  histor}'.  He  should  tell 
the  pupils  about  Columbus,  his  birth,  travels,  disappoint- 
ments, voyages,  triumphs,  disgrace,  etc.  Tell  them  of  Isa])ella 
and  her  jewels,  of  Captain  John  Smith  and  his  adventures,  of 
Pocahontas  and  her  touching  fate,  of  Henry  Hudson,  Miles 
Standish,  Roger  Williams,  William  Penn,  Lord  Baltimore, 
etc.,  and  make  the  historic  events  cluster  around  these  per- 
sonalities. Coming  down  later,  we  will  see  that  stories  of 
Adams,  Warren,  Patrick  Henry,  Washington,  Jefferson,  etc., 
will  unfold  the  history  of  the  Revolution  and  the  establish- 
ment of  the  nation.  The  stirring  events  of  the  Rebellion  can 
be  unfolded  from  a  recital  of  the  personal  actions  of  Lincoln, 
Grant,  Lee,  Jackson,  Sherman,  etc. 

Blackboard,  etc. — The  teacher  should  use  the  blackboard 
to  indicate  the  location  and  relation  of  the  principal  events. 
The  routes  of  voyagers,  the  march  of  an  army,  the  line  o( 
battle,  the  location  of  forces,  etc.,  can  all  be  represented  on 
the  board.  Historical  charts,  pictures,  engravings,  etc.,  ■vvill 
add  interest  to  the  description  of  places,  persons,  and  events. 

Outline. — The  teacher  should  have  an  outline  of  the  course 
in  the  elements  of  history  to  guide  him  in  his  work.     THi« 


494  METHODS    OF   TEACHING. 

outline  he  can  fill  up  from  his  memory,  or  by  reading  espe- 
Dially  for  the  purpose.  Such  an  outline  will  give  detiniteness 
ind  system  to  his  instructions,  which  is  a  point  not  to  be  lost 
sight  of.  In  our  Model  School,  where  the  outlines  of  history 
ire  taught  a  year  or  two  without  the  text-book,  we  place  in 
the  hands  of  our  student-teachers  an  outline  of  the  course, 
and  require  them  to  fill  out  and  follow  this  outline  in  their 
instructions. 

Children  Read  Hisfories. — Children  should  be  encour- 
aged to  read  some  suitable  books  on  historical  subjects.  It 
is  difficult  to  find  works  adapted  to  the  capacity  and  taste  of 
young  children,  many  of  the  works  written  for  this  pur- 
pose being  beyond  their  comprehension.  Abbott's  histories, 
though  written  for  the  young,  are  better  adapted  to  adults 
than  to  children.  Even  Dickens's  Ghild^s  History  of  England 
can  hardly  be  read  with  interest  by  a  child  under  twelve  years 
of  age.  Such  works  as  Miss  Yonge's  Little  Duke  and  Prince 
and  Page,  Peter  Parley's  histories,  or  Goodrich's  Child''s 
History  of  the  United  States,  may  be  read  by  children  with 
absorbing  interest.  It  will  be  well  to  allow  pupils  who  have 
been  reading  any  little  work  on  histor}',  to  relate  to  the  class 
what  they  remember  of  it.  The  teacher  should  often  read 
historic  narratives  to  the  class,  and  have  them  repeat  the 
same. 

Narratives. — The  histories  for  childi'en  to  read  should  be 
written  in  the  form  of  narratives.  Children  take  special  de- 
light in  the  stories  of  histor}'.  They  love  to  read  about 
Columbus  and  his  discovery  of  America,  about  Isabella  and 
her  jewels,  about  John  Smith  and  his  wonderful  adventures, 
about  Cortez,  and  Pizarro,  and  Alfred  the  Great,  and  Wallace, 
and  Bruce,  etc.  An  historical  story  like  The  Little  Duke  will 
be  read  and  reread  by  a  child  until  it  is  committed  to  memory. 
The  author  who  will  write  a  series  of  such  books  for  children, 
and  really  adapt  them  to  the  minds  of  children,  will  confer  a 
great,  boon  on  tlie  boys  and  girls  of  the  country. 


TEACHIXG    HISTORY.  495 

II.  Teaching  Advanced  History. 

By  the  Advanced  Course  in  History,  we  mean  a  course  in 
which  pupils  are  required  to  study  the  lessons  in  a  text-book 
and  recite  them.  The  course  should  include  the  history  of 
our  own  country,  the  histories  of  England  and  France,  and  a 
work  on  General  Histor}'.  It  may  be  more  or  less  full,  accord- 
ins:  to  the  advancement  of  the  pupils  and  the  nature  of  th( 
school.  In  treating  this  part  of  the  subject  v/e  shall  speak  of 
the  Nature  of  the  Text-book  and  Recitation  in  History 

I.  Nature  of  the  History. — The  first  requisite  in  teaching 
hifitory  is  a  good  text-book.  History  is  one  thing,  and  the 
manner  of  presenting  it  is  another  thing.  The  events  may  be 
presented  in  a  variety  of  ways,  and  the  value  of  a  text-book 
depends  almost  altogether  upon  the  manner  in  which  the  facts 
are  stated.  We  shall  mention  briefly  the  characteristics  of  a 
ofood  text-book  on  historv. 

System^itic. — The  text-book  should  contain  a  systematic 
presentation  of  the  subject.  In  the  primary  course,  history 
was  presented  in  fragments  ;  in  this  course  there  should  be  a 
narration  of  continuous  and  connected  events.  Among  the 
multitude  of  historical  facts,  this  is  not  easy  to  accomplish; 
and  the  skill  of  an  author  is  especially  shown  in  so  selecting 
and  connecting  the  events  that  the  pupil  ma}^  have  a  continued 
narrative  and  see  the  relation  of  all  the  parts. 

The  Style. — A  work  on  history  should  be  written  in  a  clear 
and  simple  style.  This  is  an  important  suggestion,  as  in  no 
text-book  is  there  a  greater  temptation  to  redundancy  and  an 
inflated  form  of  expression.  It  is  a  requisite,  however,  ofte.i 
overlooked  or  not  attained.  Many  of  our  text-books  on  his- 
tory are  so  complicated  in  their  forms  of  expression  that  the 
young  pupil  can  scarceh'  understand  them  ;  and  an  attempt 
to  recite  a  lesson  from  them  results  in  repeating,  parrot-like, 
the  words  of  the  text-book.  Even  in  the  historical  works  of 
the  sreat  masters,  tlie  style  is  often  too  ornate  and  involved. 


496  METHODS   OF    TEACHINQ. 

Macaulay's  style  is  better  adapted  to  oratory  than  history ; 
and  others  have  attempted  to  rival  his  brilliant  periods.  The 
ideal  historic  style  is  that  of  Bancroft  and  Prescott;  and  for 
school  histories  no  one  has  excelled  Goodrich. 

Leadhiff  Events. — The  text-book  in  history  should  present 
the  great  leading  events  of  the  country  of  which  it  treats.  All 
of  histor}'^  cannot  be  remembered  ;  and  the  first  object  is  to 
fix  the  outlines  of  the  principal  facts  in  the  mind  of  the 
learner.  To  burden  the  memory  of  the  pupil  with  details,  will 
result  in  giving  no  well-connected  knowledge  of  anything. 
Excessive  minuteness  of  statement  in  a  text-book  on  history 
is  always  a  source  of  vexation  to  teacher  and  pupil.  We  need 
a  skillful  grouping  of  facts,  which,  though  breaking  the  chron- 
ological connection,  shows  the  relation  of  the  events  described. 
It  is  often  well  to  distinguish  between  the  more  important  and 
the  less  important  facts  by  a  difference  in  the  type  of  the  text- 
book. Mere  epitomes,  however,  aiming  to  cover  the  whole 
ground,  are  not  satisfactory;  the  use  of  an  epitome  is  like 
giving  a  child  an  "index  to  learn  b3'  heart." 

JBiof/rdpJi}/. — The  basis  of  history  is  biography.  Every 
great  event  of  history  is  associated  with  the  lives  of  some 
great  men  who  led  the  movement.  Man  makes  history',  and 
the  centre  of  every  great  historic  event  is  a  man.  Lamartine 
says,  "History  is  neither  more  nor  less  than  biography  on  a 
large  scale."  History,  therefore,  cannot  be  correctly  written 
without  referring  to  the  men  who  created  it.  What  means  the 
history  of  the  Dutch  Republic  without  William  of  Orange  at  its 
centre,  or  the  history  of  the  Commonwealth  Avithout  Crom- 
well ?  Besides  this,  young  people  are  especially  interested  in 
the  lives  of  individuals.  They  can  sj-mpathize  with  the  actions 
and  feelings  of  a  person  better  than  with  those  of  a  society  or 
a  nation.  The  lives  of  great  men  must,  therefore,  be  inter- 
woven into  the  text  of  our  school  histories. 

Historic  Centres. — The  subject  should  be  presented  in  the 
form  of  epochs,  or  historic  centres.     In  every  country  tliere 


TEACHING   HISTORY.  497 

are  ijreat  prominent  events  which  stand  as  the  centres  about 
which  cluster  the  minor  events.  It  is  these  great  events  that 
we  need  to  fix  in  the  memory  with  their  dates.  They  stand 
as  "historical  nuclei;"  and  when  well  established  in  the  mem- 
ory, will  suggest  the  facts  related  to  them  and  growing  out 
of  them.  Thus,  the  Age  of  Augustus,  the  Age  of  Elizabeth, 
the  Reformation,  the  Crusades,  etc.,  are  suggestive  of  many 
accompanying  events  in  general  history.  In  the  history  of 
the  United  States,  such  divisions  as  Discoveries,  Settlements, 
the  French  and  Indian  War,  the  Revolution,  will  serve  as  the 
basis  of  the  historic  record. 

Li vely  Pictures. — The  text-book  on  history  should  present 
lively  pictures  of  the  past.  A  mere  dry  statement  of  histor- 
ical facta,  is  a  very  dry  thing  for  a  child  to  study.  We  need 
more  than  the  dry  bones  of  the  subject,  more  than  a  skeleton  ; 
we  need  a  body  of  facts  animated  with  a  living  soul.  History 
can  be  made  as  interesting  as  fiction,  and  if  so  presented  it 
would  prevent  our  young  people  from  wasting  so  much  time 
over  the  trashy  works  of  modern  fiction.  For  reading,  the 
historic  novel,  auch  as  Scott's,  Yonge's,  and  Muhlbach's  is 
highly  recommended  to  the  student.  The  text-book  on  his- 
tory can  catch  some  of  this  spirit,  even  if  it  must  be  more 
systematic  and  condensed.  The  events  of  history  should  be 
made  to  move  before  the  mind  of  the  student  like  the  pictures 
of  a  panorama. 

Maps  and  Charts The  text-book  on  history  should  con- 
tain carefully-prepared  maps  to  indicate  the  location  and  re- 
lation of  the  events  described.  This  is  a  very  important 
suggestion;  it  is  a  great  defect  of  a  text-book  to  be  deficient 
in  good  maps.  Maps  would -also  be  of  great  advantage  to 
the  larger  works  on  history,  written  for  adult  readers,  for  it 
is  very  unsatisfactory  to  spend  time  in  searching  for  a  map 
representing  the  country  at  the  time  of  the  events  narrated. 
Historical  charts,  either  in  the  book  or  in  the  form  of  maps  or 
atlases,  are  also  of  great  value  in  teaching  history. 


498  METHODS    OF   TEACHING. 

Illustrations. — The  text-book  on  histoiy  should  be  copi- 
ouslj"  illustrated.  Many  things  referred  to  cannot  be  de- 
scribed so  that  the  pupil  will  obtain  a  clear  idea  of  them.  A 
good  engraving  will  often  give  almost  as  accurate  an  idea  as 
the  object  itself.  Pictures  of  tlie  Indians,  of  their  wigwam-;, 
their  bows  and  arrows,  their  writing  upon  the  rocks,  etc.. 
convey  a  very  correct  notion  of  the  things  represented.  Even 
representations  of  celebrated  buildings  or  places,  portraits  oi 
eminent  men,  illustrations  of  some  prominent  event,  will  ai'i 
the  pui)il  in  gaining  a  clear  conception  of  the  subject  and  m 
fixing  the  events  in  his  memor3\ 

Wars,  Kin(/s,  etc. — School  histories  should  not  be  a  mere 
record  of  wars,  and  the  names  and  lineage  of  sovereigns. 
The  committing  of  these  to  memory,  some  one  has  truthfully 
observed,  is  in  no  proper  sense  the  study  of  history.  But  ihe 
historian  must  be  equally  careful  to  avoid  the  o|)posite  err<ji' 
of  omitting  those  great  military  events  and  characters  which 
have,  to  so  large  an  extent,  guided  the  current  of  history. 
Kings,  queens,  courts,  great  leaders,  battles,  and  sieges,  have 
so  largely'  decided  the  fate  of  nations  anil 'the  progress  of 
civilization,  that  they  cannot  be  lightly  touched  upon  by  one 
seekinsT  to  know  the  great  events  of  historv  and  undeisiuini 
their  causes,  "In  all  times  past,  the  lives  of  a  few  great  men 
have  formed  the  warp  of  history,  while  those  of  the  masses 
have  been  but  the  filling." 

Cause  and  Effect — The  events  of  history  are  the  results 
of  facts  and  intiuences  which  have  acted  as  their  causes.  Tiie 
mind,  in  contemplating  these  facts,  naturally  looks  backward 
and  inquires  after  the  events  which  caused  them.  The  student 
of  history  also  endeavors  to  penetrate  the  future,  and  predict 
the  coming  events  as  the  results  of  present  conditions.  In 
other  words,  he  delights  in  dealing  with  the  causes  and  etfects 
of  historical  events.  The  facts  of  history  thus  prepare  and 
lead  naturallv  towards  the  philosophy  of  history. 

The  text-book  should  recognize  this  want,  and  endeavor  to 


TEACHIXQ    HISTORY.  499 

meet  it.  While  there  can  be  no  formal  treatment  of  the 
philosophy  of  history,  the  general  relation  of  events  with  re- 
spect to  canses  and  effects  should  be  indicated.  The  pupil 
should  be  led  to  see  the  baneful  results  of  ambition,  the  dis- 
honor of  a  nation  through  the  violation  of  justice,  the  events 
which  brought  about  a  revolution,  the  causes  which  resulted 
in  a  decline  or  advance  of  freedom,  etc.  History  will  thus  be 
what  it  has  been  so  happily  styled,  "  Philosophy  teaching  by 
example."  It  thus  becomes  a  great  moral  teacher,  la3's  the 
foundation  of  intelligent  citizenship,  and  cultivates  an  appre- 
ciation of  liberty  and  the  means  of  preserving  it. 

General  Hlstortf. — In  works  on  General  History,  two 
methods  ma}'-  be  used,  the  ethnographic  and  the  synchr-onistic. 
The  Ethnographic  Method  describes  each  nation  in  succession 
throughout  its  entire  history.  The  S3'nchronistic  Method 
groups  the  historic  events  into  periods  or  epochs,  and  nar- 
rates the  events  of  such  a  period,  each  nation  coming  in 
where  it  belongs  in  the  period.  In  ancient  history,  the  eth- 
nographic method  must  be  mainl^^  used,  as  the  nations  were 
essentially  separate,  appearing  upon  the  stage  at  successive 
periods,  and  rarely  joining  in  any  one  general  movement.  In 
some  cases,  however,  as  in  the  history  of  the  states  of  Greece, 
the  synchronistic  method  must  be  mainly  followed. 

In  many  cases,  the  historic  movement  is  carried  along  by 
some  particular  nation,  as  the  representative,  for  the  time 
being,  of  some  controlling  idea  or  principle,  the  other  nations 
playing  a  subordinate  part.  In  other  cases,  the  nations  share 
very  nearly  equall}'  in  the  progress  of  events,  no  one  occupy- 
ing the  prominence  of  leadership  in  the  movement.  In  both 
of  these  cases,  the  sj-nchronistic  method  is  preferable.  It  is 
often  necessary,  however,  to  make  a  compromise  between  the 
ethnographic  and  synchronistic  methods. 

In  histories  written  for  young  pupils,  the  ethnograi)hic 
method  is  usually  preferable.  The  description  of  periods  will 
often   give  only  a  confused  picture  of  the  whole.     A  pupil 


500  METHODS   OF   TEACHING. 

needs  to  have  a  good  general  outline  fixed  in  his  mind  before 
he  can  well  attend  to  the  grouping.  He  must  first  attend  to 
the  order  of  time,  or  his  subsequent  reading  and  study  will 
be  embarrassed.  The  grouping  of  the  details  of  the  history 
of  each  individual  nation  around  some  central  epoch  is  similar 
to  a  srenei'alization  from  facts  in  the  natural  sciences,  and 
naturally  follows  a  knowledge  of  the  facts  themselves. 

II.  The  Recitation  in  History. — The  Recitation  in  His- 
tory should  be  modified  by  and  adapted  to  the  study.  It 
resembles  in  many  respects  the  recitation  in  geograph}^, 
though  it  is  less  technical  and  requires  more  continued  narra- 
tive than  most  subjects  in  geography'.  It  adds  the  element 
of  time  to  place,  and  thus  moves  with  a  current  of  events. 
The  subject  of  history  allows  perhaps  as  little  variety  in  the 
recitation  as  any  subject  taught ;  and  yet  it  requires  talent 
and  skill  of  a  high  order  for  real  artistic  teaching.  ^ 

Teacher's  Preparation. — The  teacher  must  be  thoroughly 
prepared  on  the  subject  of  history.  He  should  be  familiar 
with  all  the  leading  events  and  their  relation  to  ojie  another ; 
and  be  well  prepared  also  on  the  details  of  the  special  subject 
he  is  teaching.  He  must  also  be  thoroughly  acquainted  with 
the  text-book  he  is  using ;  he  must  know  what  facts  the 
author  presents,  the  order  in  which  they  are  given,  and  the 
amount  of  details  into  which  he  enters.  This  is  a  necessity 
in  good  teaching ;  no  one  can  hear,  satisfactorily,  a  lesson 
prepared  in  a  given  text-book,  unless  he  knows  the  text-book 
himself.  The  teacher  must  thus  be  master  of  the  text-book 
as  well  as  of  the  subject. 

The  teacher  should  also  be  a  good  talker.  He  should  not 
only  know  the  facts,  but  should  learn  how  to  present  them  in 
a  livel}'  and  interesting  manner.  In  no  class  is  a  ready  and 
brilliant  talker  so  necessary  as  in  history.  The  teacher  should 
have  a  fund  of  biographical  incident,  of  interesting  personal 
anecdotes,  and  a  happy  talent  for  description. 

PiipWs  Preiiuration. — In  preparing  a  lesson  in  history, 


TEACHING   HISTORY.  501 

the  pupils  should  first  read  over  the  lesson  and  obtain  a  gen- 
eral idea  of  the  leading  events.  They  should  then  fill  up  the 
details,  linking  them  in  their  proper  order.  The  words  of  the 
text-book  should  not,  as  a  rule,  be  committed ;  though  happy 
and  choice  forms  of  expression  may  be  memorized.  A  mere 
committing  of  the  language,  as  is  too  often  the  case  with 
pupils  in  our  historj'^  classes,  is  altogether  wrong.  An  effort 
should  be  made  to  see  the  relation  of  the  events  so  that  they 
are  not  remembered  as  isolated  facts,  but  that  one  fact  shall 
suggest  another.  In  many  cases,  the  writing  of  an  outline 
will  aid  in  preparing  for  the  recitation. 

Topical  Recitation. — The  recitation  in  history  should  be 
mainly  topical.  A  pupil  should  be  called  upon  to  recite  the 
first  topic,  another  the  next  topic,  another  to  take  up  the  nar- 
rative where  the  previous  pupil  leaves  it  off,  and  so  on 
throughout  the  lesson.  The  order  of  events  in  the  text  is  to 
be  closely  followed,  though  there  should  lie  no  slavish  depend- 
ence on  the  book.  The  pupils  should  be  encouraged  to  ex- 
press the  facts  in  their  own  language,  bearing  in  mind  that  it 
is  a  clear  conception  of  events  that  is  required.  At  the  close 
of  a  topic,  omissions  may  be  supplied  and  corrections  made 
by  the  class  and  the  teacher. 

Order  of  Recitation. — The  recitation  should  usually  pro- 
ceed in  the  order  of  the  occurrence  of  the  events.  It  may  also 
begin  at  a  certain  point  and  trace  the  events  backward  from 
consequent  to  antecedent.  The  former  method  is  called  the 
Progressive  order;  the  latter,  the  Regressive  order.  The  pro- 
gressive method  is  preferable  for  the  first  statement  of  the 
lesson ;  the  regressive  method  may  be  used  for  the  re-state- 
ment of  a  lesson.  The  regressive  method  is  especially  suit- 
able for  a  general  review  of  the  events  of  a  given  period. 

Qaestioninff. — At  the  close  of  the  recitation  of  a  topic,  the 
pupil  should  be  examined  on  it  to  see  that  he  really  has  a 
clear  understanding  of  it,  and  is  not  merely  repeating  the 
text-book.     The  teacher  should  see  that  he  has  in  his  mind  a 


502  METHODS   OF   TEACHING. 

vivid  picture  of  the  events,  and  not  merel}'  a  list  of  words  in 
his  memory.  He  should  be  required  to  state  the  leading 
events,  to  show  their  relation  to  one  another,  to  trace  conse- 
quences to  their  antecedents  and  antecedents  to  their  con- 
sequences, etc.  In  no  study  is  judicious  questioning  so 
valuable  as  in  the  recitation  of  history. 

Reviews — At  each  recitation  there  should  be  a  review  of 
the  important  events  of  the  last  several  lessons.  Such  a  re- 
view will  serve  to  impress  permanently  all  the  great  leading 
facts  upon  the  memory,  which  are  all  that  the  student  can  be 
expected  to  retain.  This  review  may  be  b}^  questions  requir- 
ing brief  answers,  or  the  teacher  may  require  the  pupils  to 
state  in  order  the  most  prominent  facts,  etc.  It  may  follow 
either  the  progressive  or  regressive  order. 

Xew  Matter — The  teacher  should  add  some  new  matter  at 
nearly  every  recitation.  This  may  consist  of  greater  details 
on  the  topic  discussed,  or  a  statement  of  the  relation  of  these 
events  to  contemporaneous  history,  or  the  causes  of  these 
events,  or  the  results  to  which  they  led.  The  teacher  should 
be  all  alive  to  the  subject,  and  inspire  his  pupils  with  an  equal 
interest.  Historical  knowledge,  flowing  from  the  lips  of  the 
living  teacher,  will  make  an  ineffaceable  impression,  and,  what 
is  still  better,  cultivate  a  historical  taste  and  o-jve  an  ideal  of 
high  historical  culture,  which  will  be  worth  more  to  the  pupil 
than  the  history  he  learns. 

Reading  History. — Pupils  should  be  encouraged  to  read 
more  detailed  works  on  the  subject  they  are  studying.  Of 
course,  this  can  be  done  to  only  a  limited  extent,  as  their  time 
is  required  for  their  other  studies;  but  9ven  a  short  course  of 
reading  will  do  much  to  cultivate  a  taste  for  history,  and 
awaken  a  desire  to  continue  the  study,  and  to  make  them- 
selves familiar  with  the  leading  events  in  the  histor}'  of  the 
world.  If  the  school  course  in  historj'  accomplished  no  other 
object  than  to  awaken  an  interest  in  historical  reading,  it 
would  accomplish  a  great  work. 


TEACHING    HISTORY.  503 

Discussions. — Pupils  should  be  encouraged  to  reflect  upon 
the  actions  of  men  and  nations,  and  express  the  opinions  thus 
formed.  Was  the  action  under  the  circumstances  right? 
What  would  have  been  the  probable  result  had  another  course 
been  taken?  What  do  you  admire  in  the  character  of  Colum- 
bus? Of  Washington?  Of  Jefferson?  Of  Adams?  A  discus- 
sion on  some  historical  event  upon  which  opposite  sides  are 
taken  is  also  recommended.  Such  exercises  will  give  a 
reality  to  the  study,  awaken  a  deeper  interest  in  it,  and  tend 
to  fix  it  more  permanently  in  the  memory. 

The  Dates. — The  question  is  often  asked.  Should  the  dates 
be  committed  to  memory  ?  Dates  are  necessary ;  we  not  only 
wish  to  know  the  event,  but  when  it  took  place.  Still,  all 
dates  cannot  be  remem1)ered,  and  to  memorize  the  dates  of 
isolated  events  is  worse  than  useless.  The  dates  of  certain 
leading  events  should  be  fixed  in  the  memory.  These  become 
as  centres  or  nuclei  to  which  other  events  may  be  referred, 
and  their  approximate  time  remembered.  Some  dates  should 
be  remembered  exactly ;  others  may  be  committed  in  "  round 
numbers."  The  proper  relation  of  incidents  will  aid  in  re- 
membering the  time  at  which  they  occurred. 

Cause  and  Effect The    teacher  should  cultivate  in   the 

pupil  the  habit  of  tracing  causes  and  effects  in  history.  The 
time  has  gone  by  when  a  history  lesson  should  be  made  a 
mere  recital  of  events.  We  need  not  only  to  know  history 
but  to  learn  the  lessons  of  history.  "All  history,"  says  Croly, 
."  is  but  a  romance  unless  it  is  studied  as  an  example."  Dr. 
Currie  also  truthfully  remarks, "  The  ultimate  design  of  study- 
ing history  is  not  onljp  to  acquire  knowledge,  but  to  form  the 
judgment  so  that  it  shall  be  able  to  apply  the  lessons  of  past 
tim«  to  the  present;"  and  the  teacher  of  history  should  bear 
Ihis  in  mind  and  govern  himself  accordingly.  A  fact  is  dead 
until  it  is  taken  up  into  the  organic  life  of  human  society, 
and  becomes  a  part  of  that  grand  organism  which  stands 
before  the  mind  in  a  true  conception  of  history. 


504  METHODS   OF   TEACHINQ. 

Maps  ati'd  Charts. — A  good  set  of  historical  maps  and 
charts  would  be  invaluable  in  teaching  history.  The  maps 
should  be  large  enough  to  hang  up  before  the  class  and  be  used 
in  the  recitation.  The  pupil  should  be  required  to  locate  the 
events,  trace  them  from  one  point  to  another,  show  the  march 
of  armies,  the  location  of  battle-fields,  the  wanderings  of  ex- 
plorers, the  course  of  emigration,  etc.  Charts  are  of  especial 
advantage  in  general  history,  by  showing  the  chronological 
relations,  each  nation  and  event  being  indicated  in  time  as 
countries  are  represented  in  space  on  a  map.  Progressive 
maps,  showing  the  states  and  countries,  their  extent  and 
boundaries  at  different  periods,  are  also  of  great  value. 

Lectures. — Lectures  on  history  in  connection  with  their 
regular  lessons,  or  at  the  close  of  a  school  course,  are  benefi- 
cial. With  young  pupils,  they  should  be  made  conversational, 
and  the  leading  events  be  outlined  upon  the  board  for  them  to 
copy.  With  more  advanced  pupils,  the  lectures  may  be  more 
formal  and  continuous.  No  complete  record  of  notes  should 
be  required,  as  the  attempt  to  take  notes  will  break  the  thread 
of  their  thought  and  thus  mar  the  effect  of  the  lecture.  But 
little  accurate  knowledge  of  history  can  be  left  on  the  mind 
by  a  lecture ;  the  principal  value  is  to  arouse  an  interest  and 
leave  in  the  mind  those  general  impressions  which  prepare  for 
a  more  detailed  study  of  the  subject.  The  most  interesting 
topics  for  historical  lectures  are  the  lives  and  times  of  some 
eminent  person,  and  the  development  of  those  theories  called 
the  Philosophy  of  History. 

Note. — The  Arts  of  Writing,  Drawing,  and  Vocal  Music  are  omitted  from 
this  work  on  account  of  the  many  treatises  on  tli^m  in  manuals  prepared  for 
teachers. 


msM'mmdM 


m    YB  35174 


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